DnD 5e - Movement
Dungeons and Dragons is fundamentally a game about adventuring, and adventuring typically requires movement from time to time. Even if your campaign takes place in a relatively small area, you will need to move about between various points of interest.
While these terms of not used in the official text, I find it helpful to think of movement on two scales: travel scale, and tactical scale. These are useful for conceptually separating movement across scales where distance doesn't need to be precisely measured (Travel Scale) and a scale where precise location is often important for the purposes of traps, enemies, and other dangers.
Travel scale is useful for handling movement across areas larger than a room or a small building. Even if you're just going across the street, it's often faster and just as effective to track movement on a broader, less-specific scale. Much like Narrative Time, Travel Scale can often be abstractly tracked or tracked by measures large enough that minor amounts aren't important. For example: If you're travelling 10 miles, a distance of a few hundred feet isn't important enough to track. If you're walking from one side of a castle to the other, it will probably take a few minutes and tracking your foot-by-foot movement is both tedious and rarely important. Even if you're just crossing a 10 by 10 room, you can often track movement on "Travel Scale" so long as there's no chance of anything violent or dangerous happening.
Tactical Scale is typically used for combat or for exploring dangerous areas like dungeons where any given 5-foot square might set off a trap or someother hazard, and where your precise position is important in the event that you stumble upon a hostile creature and combat breaks out. At this scale movement is often slow in real-world time, but this is a scale at which you should move cautiously and deliberately, watching your surroundings constantly for signs of danger.
Nearly every creature (with some very unusual exceptions) has a Speed. This measures the creature's ability to move during a single turn in combat, and Speed is always measured in feet at 5-foot steps, so a creature might have a Speed of 30 ft. or 35 ft., but you will never see a creature with a speed of 32 ft. or any other amount that can't be evenly divided by 5.
Dungeons and Dragons presents four types of movement, each of which work a little bit differently, but the primary difference is how they allow a creature to move. All creatures have a land speed listed in their stat blocks, but creatures without the ability to move on land (like fish) typically have a listed land speed of 0 ft.
Land Speed is the most common type, and represents walking, crawling, slithering, or any other type of movement which takes place on a mostly horizontal surface. Humans have a land speed of 30 ft.
In many cases the official rules text will specify "speed" without specifying a type, which is often confusing. In general, if something gives you a speed (such as your character's race) without specifying a type, it's a land speed. If an effect modifies your existing speed (such as the haste spell or the Barian's and Monk's speed bonuses) it applies to any movement type which your character has naturally (such as land speed for a human or swim speed for a fish), but not to any additional movement types which you might have (such as a fly speed granted by a spell).
Burrow Speed represents a creature's ability to move quickly underground by burrowing. This is typically limited to moving through "loose earth" such as sand or dirt, but creature's can't burrow through solid stone without an ability which specifically allows them to do so such as the Earth Elemental's Earth Glide ability. Moving this way does not leave a tunnel or other passage unless the creature has an ability which causes it to do so, such as the Purple Worm's Tunneler ability.
For more on Burrow speeds, see page 8 of the Monster Manual.
Climb Speed represents a creature's ability to climb vertical surfaces. While nearly all creatures can climb, creatures with a climb speed are abnormally good at it. For these creatures, moving up a wall is as easy as it is for a human to walk on even ground. These creatures include creatures like monkeys and spiders.
Some creatures also have the ability to climb upside down on horizontal surfaces. This usually comes from the Spider Climb ability or from the spider climb spell.
Even if you don't have a climb speed (most Player Characters won't), you can still climb most of the time. Doing so costs 2 ft. of movement for each 1 ft. moved, which essentially means that you move at half of your speed while climbing. If the surface is difficult to climb, the Dungeon Master may require a Strength (Athletics) check to climb the surface. If a surface is impossible for you to climb, such as a perfectly smooth wall, the DM may simply disallow climbing it.
For more on climbing, see page 182 of the Player's Handbook. For more on Climb speeds, see page 8 of the Monster Manual.
Fly Speed represents a creature's ability to move through the air, by either mundane wings like wings or by magical means like spells. Creatures are free to move up or down, to change directions in place, and to hover in place regardless of real-world physical complications like momentum and thrust.
Despite the clear advantages of flight, it also has some risks: If a creature's fly speed is reduced to 0 (such as if the creature is grappled, restrained, or paralyzed) or if it is otherwise unable to move, it falls unless it has the "Hover" ability or it flies magically. If a creature has a fly speed and the Hover ability, "(Hover)" will be displayed following the creature's fly speed. For more on falling, see Falling, below.
For more on fly speeds, see page 191 of the Player's Handbook and page 8 of the Monster Manual.
Swim Speed represents a creature's ability to swim through water and other liquids. While nearly all creatures can swim, creatures with a swim speed are abnormally good at it. For these creatures, moving through water is as easy as it is for a human to walk across even ground. These creatures include creatures like fish, whales, and tritons.
Even if you don't have a swim speed, you can still swim most of the time. Doing so costs 2 ft. of movement for each 1 ft. moved, which essentially means that you can move at half your speed while swimming. If the liquid is difficult to swim through, such as a fast-moving river, the Dungeon Master may require a Strength (Athletics) check to swim safely.
For more on swimming, see page 182 of the Player's Handbook. For more on swim speeds, see page 8 of the Monster Manual.
Mixing Movement Types
In many cases, you will encounter "difficult terrain". Diffcult terrain costs 2 ft. of movement for every 1 ft. that you travel through it, effectively meaning that you move at half speed through difficult terrain.
Difficult terrain can take a variety of forms. At Tactical Scale, this typically means rubble, uneven ground, heavy foliage, or some other impediment which you can't simply walk or run through. At Travel Scale, this might be marching through a forest or through rocky terrain with frequent elevation changes.
Moving long distances between locations requires travel of one kind or another. Though walking overland is common, you might also ride on horseback, in a wagon, or aboard a ship. At higher levels you might gain the ability to fly overland using spells like air walk, magic items like a flying carpet, or special mounts like griffons or pegasi.
The minutiae of traveling long distances are covered on page 181-182 of the Player's Handbook under "Travel Pace". You don't need to know these rules off the top of your head, but you'll want to reference that section whenever you're traveling long distances. The official text also covers the mechanics for things like foraging, drawing a map as you travel, navigating to avoid getting lost.
One important things that may be helpful to know off the top of your head: all creatures travel at roughly the same pace, regardless of their speed. This requires some suspension of disbelief since creatures with 5 ft. speed move as fast as a horse as the rules are written, but it also makes it much easier for halflings in your party to keep up with everyone else.
When moving between locations, it can be helpful to establish a "Marching Order". This is helpful for the Dungeon Master to know roughly where everyone in the party is positioned in the event of an ambush, a trap, or another hazard.
This could easily be called a "formation", but the term "Marching Order" dates back to Dungeons and Dragons' earliest days, where marching single-file through narrow dungeon corridors was the defining mode of travel. Now adventures take place in more diverse locales, but the term "Marching Order" has stood the test of time.
A marching order is divided into one or more "ranks". The front and back ranks can hold as many members as can fit side-by-side, while middle ranks can fit as many members as you like. If you only have two ranks, they are by definition front and back ranks.
While you're traveling in open areas like along a road or through a field, you have plenty of room to freely form your Marching Order, so you might choose to have a dozen characters in the front rank while leaving just one in each of several other ranks. In a narrow dungeon corridor, you are much more restricted: you might even be forced to march single-file, putting one character in the front, another in the back, and the rest of the party in any number of middle ranks.
When deciding who to place in each rank, it's helpful to consider two factors: The characters' Passive Perception, and their ability to survive unexpected hazards like a sudden monster attack or an unnoticed trap. Noticing a problem before it affects you can prevent a lot of trouble, but if you don't see something coming you want whoever is in the front and back ranks to survive whatever hits them. Frail characters who have low HP or poor AC should typically be placed in the relative safety of the middle ranks.
If you're having trouble visualising marching order, consider a group of people walking on a sidewalk. A small group may be able to stand side-by-side, forming a single rank. However, if the sidewalk is too narrow, the group may split up into multiple ranks of people standing alongside each other. A few people might form a front rank, typically choosing the direction of the group as a whole. Depending on the size of the group, one or more groups of people might form middle ranks. Finally, one or more people will form the back rank, marking the rear of the group.
You may perform either a high jump or a long jump. You may perform a long jump to move horizontally a number of feet equal to your Strength score, and you may perform a high jump to move a number of feet equal to three plus your Strength modifier (not your Strength score), provided that you move 10 ft. along the ground immediately before performing either kind of jump. If you perform a standing jump, these distances are halved.
There are some additional specifics to the rules for jumping, so if you need to know things like how high you can reach with a high jump or how high you jump with a long jump, see page 182 of the Player's Handbook.
While in combat, you may jump as part of your normal movement during a turn. Any horizontal distance that you travel while jumping counts against your movement for the turn just like walking would. If you attempt to jump and run out of movement, your jump ends at the limit of your movement. For example, if you have a speed of 30 ft. and a Strength of 10, you can jump 10 ft. following moving 10 ft. on the ground. If you moved 25 ft. before jumping, you could only jump 5 ft. before exhausting your 30 ft. of movement. However, if you take the Dash action to gain additional movement (giving you a total of 60 ft. of movement for the turn), your jump could continue and you would still have 25 ft. of your 60 ft. of movement for the turn. You probably even have enough room to get another 10 ft. running start before performing another jump, provided that the terrain cooperates.