A group of strangers have very little motivation to fight and die alongside each other. Every party needs something to tie it together. By establishing some basic relationships at the beginning of your campaign, you can give your party a decent reason why they should be working together.
Each player should pick one other party member with whom to have some sort of social tie. They could be family, they could be friends, or whatever else fits the characters. These relationships should be agreed upon by both players, and two players may not pick each other. The proposed tie should not require any active effort on the part of the recipient. This should leave each character with one or more ties: one that they proposed, and possibly one or more that someone else proposed to them.
Multiple players may establish a tie to the same player. Maybe that character is the social focal point of the group, or maybe they are a leader or officer of some sort. Character with more ties might be more socially active, more important, or just better connected. Characters with only one tie might be less well-liked by the rest of the group, they might be particularly shy, or they might just not have gotten to know everyone yet.
Avoid creating "islands" within the group: groups of characters who lack ties to another group of characters. This should only be possible with groups of 6 or more since two players may not both propose a tie to each other. Of course, in large groups you might intentionally create "islands" like this in order to create interesting conflicts within the party.
Each player should pick one party member with whom to establish a point of contrast or conflict. The target character generally should not be the character's only tie if the originating character has only one unless they intentionally want the character's place in the party to be contentious. Contrasts should be relatively minor compared to ties in most cases. If one character actively hates another, it an cause problems during play which might disrupt the game in ways that aren't fun. If one character secretly hates another character's after-shave, it can be an amusing recurring conversation point, but won't actually cause the players to actively hinder each other.
Characters who are the recipient of multiple contrasts might be difficult to get along with, or are otherwise unpopular. Try to avoid having one character be the subject of all of the party's contrasts. This can make one character (and potentially the player) a pariah within the group.
- Dyson's Dodecahedron: The Full Fiasco-Based D&D Starting Set - Based on Fiasco's rules, Dyson created a simple table of random character relationships which can be generated by rolling 2d6 for each relationship. These relationships are perfectly viable for Ties, and can be adapted to be used as Contrasts.
- Dungeon World - Dungeon World includes rules for "Bonds", which are similar to Ties and Contrasts. The example Bonds listed under each class's description would make excellent examples of Ties and Contrasts.