OK, you have two options:
1. Keep the fish in the current tank while you do a fishless cycle on the new tank by adding ammonia. Advantages of this: the new tank would be fully cycled when fish are added. Disadvantages: you would have to keep them in an uncycled ten gallon while yuo cycle the 29G (which can take 6 weeks). The fish will really suffer in the uncycled 10G.
2. Move fish and old filter straight to the new tank (use the new filter also). You will then have to cycle the new tank with fish. Advantages of this: although still in an uncycled tank, it is larger and waste is diluted.
I recommend the second option. Because you will still have fish in a cycling tank (regardless of which option you choose) you will have to test the water daily (for ammonia and nitrite) and do waterchanges whenever the levels for either are above 0.5ppm. so, a test kit is essential. Make sure you buy one when you get the tank at the weekend. (buy a liquid one, not strips)
The tests will tell you how much and how often to change the water. If ammonia is 1ppm, you need to do a 50 per cent water change. For the first couple of months it is likely that you will be changing water very frequently (maybe daily) but once the tank is cycled (tests show 0 ammonia and 0 nitrite) you only need to change the water once a week, changing about 25% at a time.
Makes sure you add declhorinater when you change the water.
Also, if you don't have one already, buy a gravel vac (it's a syphon-type thing). Manual is fine, you don't need battery-powered. You use the gravel vac to do water changes, and whilst you remove water you also vacuum the gravel, removing all the uneaten food and waste. This will help to keep ammonia levels down. Also feed lightly for now, this will also help to keep ammonia levels down.
It might sound like a lot to buy, but all of it is essential. Things that aren't essential are ornaments and even gravel (a lot of people have bare-bottomed tanks). So you can wait and make your tank look pretty later, for now make sure the money goes on the essentials to keep the fish happy and healthy.
I know this is a long post, but it should help. If there's anything you don't understand let me know and I'll try and explain it a bit better. There's a lot to learn when you start keeping fish. One good thing though, when it comes to studying the Nitrogen Cycle at school, you'll be great at it!
Good luck

post back with any questions