How do I sync a new iPad that I've already started using, and don't want to lose the data?

Question

I have a new-ish iPad that I have started using without syncing to iTunes.
I now need to sync iBooks, if that is possible, with my iPhone. I gather that the best way to do this is to link the iPad and iPhone up with iTunes.
When I plug the iPad into my iMac, it appears as though it will delete all the existing content on my iPad as it thinks it is a brand new, unused iPad. I don't want this.
How do I connect the iPad to iTunes for the first time, without it erasing what I already have on it?

Answer 1

Sadly, none of this works.
I have backed up using PhoneView and iCloud. When I plug the iPad in, I can't access anything other than a binary option that says 'set up as a new iPad' or restore from a previous back-up. Sadly, none of the iCloud back-ups that I have done from my iPad appear in the list.
Looking at the list provided above, I can only do steps 1-3.
4. Store>Authorize this computer.
- This doesn't work. A pop-up appears saying that I have already authorised 4 devices. It won't let me do anything else with this.
5. File>Transfer Purchases(To make sure all purchased content on your phone will be in your iTunes library).
- Greyed out - can't do this.
- None of the things below therefore work either.
6. Right click your phone in the left device pane & select "Reset warnings".
7. Right click again and select "Backup".
8. Right click again & select "Restore from Backup", select the backup you just made. When prompted to create another backup, decline.
9. This MUST be followed by a sync to restore your iTunes content, which you select from the various tabs, You'll get a popup regarding your contacts & calendars asking to merge or replace, select "Merge".