iPhone upgrade without deleting data
Okay, let me walk you through it step-by-step. The first thing we'll need to do is sync. Then we will backup, and then put the new OS on.

Syncing


Take your iPhone and plug it into your computer (using the charging cable that came with it)(it should have a USB, and iPhone connector)
If iTunes does not automatically pop-up on your computer screen within 1 minute of pluging in, click the icon for iTunes on your computer.
In iTunes, your iPhone should pop-up after a few minutes. Make sure that you are syncing all that you will want when the whole process is over. Go to the different tabs on top to make sure that you are syncing apps, notes, calendars, etc... Once you know that you are syncing all that you want, you must look for the sync button (it should be located at the bottom-right of iTunes within your device "Summary" page). Click it.
To be extra careful, once the sync is over, you should click sync again (this will ensure that you have successfully synced your iPhone).


Backing Up


Now you will want to Backup your iPhone to make sure that you won't lose any of your note, calendars, and so on. To do this, click the "Summary" tab in iTunes which will display a picture of an iPhone. After this, scroll down to the "Backups" section of this page, and finally, click "Back Up Now".
Once this is done, you should probably do it again to ensure that your information has been successfully backed up. Just follow the same steps above.
Finally, move on to the step shown below.


Upgrading iOS


Now, in the same "Summary" page, scroll down to the "Version" section of the page. In here (IF YOU HAVE COMPLETED ALL STEPS ABOVE), click "Check For Update". In the window that appears, click "Download and Update".
Confirm all of the following prompts that appear (Terms and Conditions, and so on...), and let it do its thing.
Have a cup of Hot Chocolate and wait for the download to finish. Once this has occurred, confirm any other prompts that appear (if they do).
Watch a little TV while you wait for the OS to update into your iPhone.
Once it is done doing this, it will restore the information into your phone and do a sync automatically in order to put in your apps and everything.
Once you get any indication that it was finished (MAKE SURE THAT IT IS FINISHED)(IT USUALLY TAKES ABOUT A DAY FOR THE WHOLE PROCESS TO FINISH), unplug your phone and enjoy.
Take a break! Go to bed, have a cup of tea, whatever! You now feel wiped out, and wish you never had asked...Don't worry about it, you now have the latest iOS.