You can increase friendship by getting companionship EXP, which can be earned by the following:
- Completing daily commissions and then turning in the commissions to Katheryne, who is located in either Mondstadt or Liyue Harbor.
- By doing domains and ley lines.
- Fighting the various weekly bosses.
- Doing the random events and quests that show up.
Remember, when doing these you must have the characters that you want to increase friendship with in your current party, as you can’t increase friendship level if you aren’t actively using them.