I'm elaborating on ChrisF's answer of building in moderation tools. This is important. But, that's not all there is to it. Every piece of forum software I've used has the ability for users to flag a post (usually for spam). Smaller sites, in general, don't use this feature that often.
Why? I suspect, it's because moderation is taken care of for users. What does it do for me to flag this post? Does it disappear immediately? Usually not. It still needs someone to come along and accept the flag.
Adding in another aspect to this self moderation is important. Gamification. If you do something that helps the site, the site administrators provide you with something in return: a shiny pixel; a slightly larger number; a way to show that you are winning the internet (or at least this small corner of it). The Discourse forum software does the same thing. You've helped this community grow? We will trust you just a little bit more by providing you with more benefits.
What do you do if you aren't on a platform that supports this kind of reward system? Make one, manually. Publicly acknowledge your users that are helping to moderate the community. Do you have 5 users that vigilantly flag every spam bot that posts on your PHPBB board? Thank them. Do you have a user that monitors your support subforum and diligently helps every poor soul that wanders in? Thank them too.
It's amazing what a little, intangible, reward can do. It helps people feel part of the community and it raises their reputation in the eyes of the community.