How does someone earn your trust?
Don't lie, have a good personality, and don't be an idiot.
Personally, I trust somebody when I know them for awhile. Also, I can tell by their personality, how they act, and talk.
They Don't lie, break rules..
I must know them for a while for them to get my trust. I give people a chance instead of just rejecting them right away because I don't know them.
Once me and he/she are friends I slowly give then trust depending on how long I've known them for. After a while they gain almost all of it. Notice not all of it because this is a game, but people only lose trust from me if they did something that'd make me double think of the person. I do give my trust back, but that's after I see they are truly sorry for what they did and after some time of just a little trust. :P