How can I choose to trade with other survivors in State of Decay so I can earn their trust? I have done it before but it was mission involved. I mean, we should be able to do this without being on a mission, otherwise the survivors are useless.
Short answer: You cannot initiate trade or any mission by yourself. Trust can only be earned by doing missions they randomly give you. It's either Trading, breaking a Siege, escort one of their missing survivors home, etc.
Enclave survivors are your potential housemates. When their Trust become high enough (they become Friendly Survivors), you get the option to ask them to join you for no cost.
While you cannot directly trade, you can put stuff in and take stuff out of their lockers, just like your home base (which cost less Influence if they trust you more and vice versa). As for resources trading, it will always be your ammo for their food/med, since ammo is supposedly the most needed resource.