As I was reading through posts for this tribe I saw a lot of folks embarking upon their first half marathons who are looking for some training tips and wanted to offer up a great resource site that has helped me along the way.
Instead of trying to rehash a lot of information I thought the least I could do is provide this link to a section in the runnersworld website (below) which has some OUTSTANDING training plans for your initial foray into the joy of the 13.1 miler. I have followed a couple of these plans and they definitely helped me in preparing for different events. I will add that in between events I have started to utilize 1/2 mile repeats to aid in increasing my overall speed. This is a work in progress but it's promising so far. Read my short description on this technique here: Become a Stronger Runner This can be easily ( well, there IS a little sweat involved :) applied to increasing your 1/2 times as well but you need to have the distance base and endurance before incorporating this.
Although there are lots of sites on running this is one of my favorites as it is very straight forward and has information from beginner to advanced that is sure to help you.