Update: The more I think about this, the less comfortable I am suggesting it. While I would do it myself a little digging around has me uncertain that it would go smoothly, and I'd feel pretty rotten if I got someone into a mess. There are several third party solutions (some free) that promise to transfer your iTunes library to a new computer. My recommendation is to research those and pick a good one. Or maybe someone here has experience with one and suggestions.
The easiest way only works if you are going from PC to PC, or Mac to Mac.
Find the iTunes library folder on your old computer. Copy the entire thing to an external hard drive. You can also put both computers on the net and copy the folders over that way. But if it's a big folder it will only take a little less long than forever.
Load and run iTunes on the new computer. Find the iTunes folder it created it. Delete it and replace with the folder from the old computer.
Run iTunes, got to the Store menu and choose Authorize This Computer. Test your ability to play your music.
If you are getting rid of the old computer be sure to open iTunes, go to the Store menu and Deauthorize This Computer. You only get to authorize 5 computers to an account. While there is a way to remove excess computers after the fact, it's a bit of a pain.
If everything you want is already on you iPad, you can just plug it into the new computer with iTunes, refuse the overwrite option, then go to the File menu, and choose Transfer Purchases From. . .
You'll still have to authorize the computer.