As is true with any other relationship, trust must be earned. I feel that one of the reasons that it can take so long to book a job as an actor is that you must show people that you can be counted upon to be professional and do a good job. If you're hired by a casting director, even if it's just background work, they are counting on you to do your job and do it well! If you don't show up for example, it reflects badly upon your reputation, and also the person who hired you in the first place.
So, when I hear people in LA say "it's all about who you know", that really isn't true at all. You can know a LOT of people in the entertainment biz. But it's the ones who know YOU that can help you get to where you'd like to be in this crazy biz. I suggest following up with casting directors often. Always show them that you're a professional and that they can count on you. Bottom line with every relationship is: be honest, be kind, and do the best you can do! That is the best way to achieve a good reputation among your peers and co-workers. :)