The usual troubleshooting steps when it comes to iPhones are (stop at whichever step solves the issue)...
1) The old classic IT "Turn it off and on again".
2) A full reboot of the phone (hold down the home and lock buttons at the same time until the screen goes dark) - usually takes a few minutes to complete the reboot but it often cures these sorts of niggles. (This has normally always sorted out my occasional issues).
3) A full restore in iTunes - just connect up to your computer, allow the iPhone to sync in iTunes and then press the restore button on the iTunes iPhone page. iTunes will do a full backup and then reinstall the OS on the phone and then ask if you want to set up as a new phone or restore from backup - normally you would want the restore from backup! You will then end up with everything back on the phone the way it was (settings, messages, contacts, photos etc.).
4) If restoring from backup doesn't work then you might try the restore process again but setting up as a new phone instead, just in case there is something in the backup data that is causing the issue - you can then resync all your music, apps etc. - but you won't have your text message history, all your settings will be set to default (including wifi passwords etc.) and you will need to have manually backed up your photos and then resynced them as separate folders afterwards. You can always restore your previous backup though if even this doesn't work - and then you will have everything back the way it was before you set up as a new phone (iTunes will typically keep the last few backup images and you can choose which one to restore). Personally I wouldn't normally bother with this step but if your nearest Apple store is a way away then it might be worth it.
5) If that still hasn't helped then it is probably time to book an appointment at your nearest Apple store's genius bar - they can usually sort out any issues and will be able to issue you with a brand new replacement if appropriate (if you are still within warranty of course). Alternatively you can try whoever you bought the iPhone from (if it wasn't an Apple store), though typically this will involve sending your iPhone away rather than having it fixed or replaced on the spot as you would get in an Apple store.
