Hi Sarah. Welcome to the site, and congratulations on your half marathon! I think you turned in a perfectly respectable time, particularly for your first time out.
Since you've now completed a half, I'm going to assume that you have a reasonable mileage base (somewhere in the neighborhood of 20 miles per week). If that's the case, you're likely ready to begin incorporating some speed work into your training routine.
I tend to think of interval workouts, which consist of periods of fast running interspersed with more relaxed running to allow your muscles to recover and so you can catch your breath a little bit. For instance, you might look at doing one workout a week consisting of repeating the following between four and six times: run one lap around a track (about 400m) at a pace between 11 and 11:36 min/mile followed by a lap of easy jogging. After doing this for a couple of weeks, try doing the same thing with a longer run: two laps around the track (800m) at a pace between 11:30 and 12:02 min/mile with one lap of easy jogging in between (repeat four times or so). These workouts will force your body to adapt to moving faster. Try not to do interval workouts more than once a week -- they put quite the beating on your body!
You can also start incorporating tempo runs into your routines. These are designed to build your body's ability to sustain higher speeds for longer while processing lactic acid more efficiently. The key here is to push yourself at paces that are a little faster than are comfortable, but are below your body's ability to clear lactic acid. This takes some getting used to, but a good target pace for you might be in the neighborhood of 12:44 to 13:17 per mile. Try that over six miles or so, and you'll definitely feel like it was a workout!
These are just some general suggestions; you might benefit from looking at a more structured training program (e.g., something from the SmartCoach at runnersworld.com, the FIRST half-marathon or marathon training programs, or any of several programs you can find here at active or around the web). Incidentally, I didn't just make up those target paces for your workouts. They're based on plugging your half-marathon time into the McMillan Running calculator (at mcmillanrunning.com).
After you've run a few more races (or benchmark runs), you can plug in new times and get new targets for your workouts.
Good luck, and post back often! Feel free to join the existing threads, as well. I post in the Long Haul thread, and there's also another very active thread for half marathoners in training (though there are plenty of people who have finished their halfs and hang around).
Don