Well. One thing I learned after having my phone for like 2 months is that if you hold the power button in you can actually turn the phone off completely.
Make sure you hook it up to your computer regularly to get updates, I don't know if yours will have the most current one.
Keep your location services setting off unless you need it. Same for 3g network. They can drain the battery big time. You want to let the battery drain completely without recharging about once a month to prolong the life of the battery.
Get the Shazam app. Its amazing. It listens to a song playing and then tells you The Artist, The Album, The Name, and I think its going to show lyrics soon -- the song just has to be available on itunes. It tells you all this after you press tag in about 20 seconds.