Before anything else, go into any app that has important documents and see if you can email or otherwise save them off the iPad. You can always get your apps back, but if something goes wrong the contents of those apps will be lost.
Go into iTunes Preferences, the Devices tab, and turn off auto-sync. That will stop the iPad from trying to sync immediately.
Now plug you iPad into the computer. If/when the sync dialog comes up, choose Transfer Purchases instead, if offered. Otherwise close out of the dialog, right click on the iPad under the Devices list, and choose Transfer Purchases. This may take a long time if you've got a lot of iTunes, App Store, and iBooks stuff on the iPad.
Do not sync.
When it is done go though the Media in iTunes on the computer and make sure what you wanted got transferred. If not, give it another go.
Do not sync.
Go through all the sync option pages one by one and make sure they are set up the way you want. Leave the Info page alone for now. Pay close attention to the Apps page. Make sure you are set to sync apps. Make double sure that the important app containing the important documents has a checkmark next to it as well.
When ready, go ahead and sync.
The first part of the sync will be a backup. It is important to check your iPad after the sync and make sure the important document(s) did not go bye bye. If they did you'll want to do a Restore from Backup, not another sync. If you sync again, then the new backup will overwrite the old one.
With only a slight amount of luck you'll be good to go. Well, maybe your media is a little scrambled, but since it's all on the computer you can sort that out later.
One last note. If you've got photos on the iPad that are vital (no other copies) you'll want to use an app like PhotoSync to copy them to the computer first. It is almost impossible to keep previously synced photos on an iPad when setting it up with a new computer, but as long as you have copies, you can always get them back on later.
