Yeah, as long as you're on an official carrier and don't need to unlock your phone.
1. Sync/backup in iTunes. Your purchased apps will transfer over.
2. Update iOS. (I usually download the ipsw first, then do a Shift/Restore, but whatever way you do it is fine.)
3. Here you can either jb with redsn0w first, or do your restore from backup. I usually restore first, I think, since iTunes will probably prompt you to do so once the iOS has been updated.
4. Once everything is synced back, close iTunes and run redsn0w.
Issues you may run into:
-If you get errors in iTunes, it's almost always due to your hosts file being changed in the past due to some other jailbreak activity. If you've ever used Tiny Umbrella, be sure to open that before doing anything else, click Advanced, and uncheck the "Set hosts to Cydia on exit" box. Doing this will allow your iPhone to be verified by Apple when you update--you want this when you're using the current firmware.
-When you restore your backup, none of your Cydia apps will be there. You'll need to reinstall those after you jb and reinstall Cydia. This is normal.