The trust system works in that if you support your team mates they will get a liking towards you. Something that is frustrating is if you shoot your team mates they lose trust in you. No matter how careful you are they will walk into your line of fire. Just take extra precautions, and move away from your team. You support your team mates in that when they talk to you, you don’t walk away, I did this to Charlie and I lost trust. Just sit back and listen to what they say. You kind of have an idea of each characters personality, so if Bo talks about picking up Hookers you go for it. If Faye talks about you being a player even if you are, just say no. Support them and always agree usually. Make sure to read carefully. I agreed with Bo that Faye had a nice body and I lost trust in her. So if one member talks about someone behind their back and that person is not around agree. You will gradually get the hang of it. The times that you walk slowly and your team stands around and this is usually all members, go talk to each, they will either have a conversation and this will build trust or will just say one line. This is when you enter the underground city after fighting the spider and also once you come out of the sewer into the upper city. When you go to chapter select and do a mission, your trust level will be at the base point.
It is best to stick with the same people to build up their trust. I chose Bo and Faye. Now this is a little trick to build up other people’s trust. This is in chapter 2 so you won’t have Cain or Shindo. As I had Faye and Bo in the sewage treatment plant, Charlie and Rachel did their own thing. You have to go save them once you do and you get to the elevator DO NOT hop on. An infinite amount of Crazy monkey bots will spawn. Just keep shooting the monkey bots and melee when they get to close. You get heaps of doubles, triple and even multi-kills. Just keep killing them, Charlie and Rachel will be very impressed by your awesome killing. I never picked Charlie or Rachel so I had the lowest trust levels with them and I got their trust almost all the way up (I ran out of ammo, so I recommend you fully stock up). This doesn’t have to be Charlie and Rachel, it can be anyone. It will all depend before you enter the sewage treatment plant as your 2 team members go off and you save the other 2. This is A LOT easier on lower difficulties so you can come back to chapter 2.
Please see "MAX trust:Cain" and "MAX trust: Shindo" for another method.