1. Get a good case. Read reviews. Be wary of overly-minimalist cases and cases that don't offer much friction/grip. You probably already did all of this, but I want to re-emphasize the importance.

2. Take full advantage of the interfaces you can easily get to by swiping from off-screen. Swiping up from the bottom gives you quick access to control brightness, turn on/off the flashlight, and use the camera (among other features). Swiping down from the top gives you a quick summary of what your day looks like, according to Apple; itinerary, weather, etc., and you can customize what data it will fetch for you on this menu somewhere in the "settings".

3. If your hands are full or you're driving, look for the little (very little) microphone icon button that appears when the keyboard displays for text entry. The speech-to-words translation is pretty accurate.

4. Double tapping the home button allows you to see what apps are currently running. After double tapping, if you want to terminate a particular program/app, scroll over to it and flick it upwards and off the screen to close it. This can be good if you're running many intensive apps all at once, and need to close some so that you free up the memory (it takes a LOT of apps running to necessitate this).

5. Holding the home button for a few seconds (at the "home" screen) will allow you to permanently delete applications and/or move the icons around on the home screen.

Most importantly, don't be afraid to push all the buttons. You're not going to break it by using it. Apple has made such a thing very difficult. You'll be up to speed in no time :).