The best way to build ANY relationship is organically. :) Find out who you know in common and get introduced. Find out what you have in common so you have something about which you can relate, without it always being about how THEY can help YOU get your next gig. Remember, if you're an actor, you're helping filmmakers and casting directors solve a problem, every time you are the right actor for the role.

So, the goal is to get on the radar of the folks whose problems you solve. If you remember that MOST actors "lead with the need" and instead "lead with confidence and an awareness that you help us solve a problem," you'll stand out and stay on our mind when your "answer" lines up with our "problem."

Set up Google Alerts for the top ten folks you're targeting (research will help you get that list of folks down to ten) and find ways to intersect at networking events, panel discussions, workshops, etc. Keep 'em posted on your work in the industry (so they know you're out there makin' it happen) and take a long-haul approach to relationship-building in this industry.

If you look at it as: "We're in this for the next several decades together as collaborators," it becomes a much less daunting task. :) Good luck to you!