It all depends on where you start -- the 30-40 miles a week already mentioned may be too much if you're not at that level yet. First, pick a distance that is a little further than you can already run without a rest -- if it's a mile, try a mile and a half...if it's three miles, try setting it at four. Start out at very slow speeds (for me that was the hardest bit...slowing down) until you can run that entire distance without a rest. Once you've achieved that, gradually increase the speed until you can run that distance in the time you want to average per mile for the half-marathon. Be realistic about that time. After you're up to the desired speed for this shorter length, increase it by another half-mile or mile and repeat the process.
Generally you don't want to make your distance using this process any more than about 10 miles since it will be done a few times a week, though about once a month or so there's nothing wrong with challenging yourself to run the entire half-marathon distance on your own to gauge how you do. Many people also like to build up their strength using varying terrain or varying speeds throughout the run. Just remember that the primary point of a marathon or half-marathon is stamina -- there is no benefit for being the fastest person in the first five miles and then being unable to continue.