A half marathon is a brill distance to run - you can train for it without the training taking over your life (like a marathon), and it's a relaxed 2 hour poddle and you're finished before you feel like you're about to die.
Remember that when you're training you need to run at training pace, which is NOT race pace. It's slower - about 10% slower. Time yourself on your training runs and ensure that you're running about 10% too slow to hit your target time. You can either train slow and far, or fast and short (like speed training), but if you run fast and far then that's racing, and it's punishing on your muscles. You're asking for injury if you try to train too fast.
So, to getting your distance up:
You need to get yourself able to run about 7.5 - 10 km relatively comfortably by about 14 weeks before the race.
In the last 14 weeks before the race, you should run 4 - 5 times a week: 3 - 4 training runs of about 7 km, and then one long run (typically on the Sunday). Your Sunday run is where you start ramping up your distance. Start from your 7.5 km or so, and ramp up to about 17. Do it gradually so that you run 17 km twice before the race.
Ramp up so that you peak at a distance, then drop back and ramp up again to a higher peak - this gives your endurance a chance to build gradually.
For example, this is a nice build up:
Week Distance
1 7
2 8
3 9
4 10
5 8
6 12
7 14
8 10
9 15
10 17
11 10
12 17
13 5
14 Race!
This way, race day is the first day you actually run the full distance. There are people who get themselves to the point where they do the whole distance in training, but you don't need to - it's harder, and if this is your first long race then why not save the triumph of doing the distance for the actual day?
Top tip: carrying water with you is a PAIN when you're doing distance, and carrying enough for a 2 hour training run is even harder. When you're planning your long runs, take a small bottle but ensure that you have places en route where you can top up.
Sorry this is long - I like to run