For me trust is something that builds and deepens over time by going through and working through all of the things that happen between people in relationships; the misunderstandings, miscommunications, times of need, respect, support, loyalty, confidant, etc., etc.. In the beginning of any relationship whether it be romantic, friendship, or colleague, I test the waters to determine whether or not the person can be trusted and in what ways they can be trusted. This way I find out early on whether or not I can trust the person so I can determine how much to invest in the person and the relationship.
If someone shows me in the beginning of a relationship that they are not trustworthy more than likely they will not be trustworthy down the road either. I also listen to what my gut feelings tell me about a particular individual. If I get an uneasy feeling about someone, even if I can't put it into words, I have learned to heed those warnings as they have been right more often than not.