The balloon tracking systems I've seen on the internet use an altimeter, GPS and a radio or cell phone link (SMS I think) to a ground station, which then puts the data on a web sight. However, I am just a casual reader going from memory. There may be a better solution.
Off hand I think you will need to know how to:
- Get data from a GPS module and an altimeter or pressure sensor
- Send data out over radio or cell system
- Receive data from radio or cell system on a PC
- Automatically update the data on a website
There are a number of tutorials for reading analog inputs and interfacing Arduino to GPS module. I know I've seen some cell phone shields, so there should be some help with that as well. I can't help you on the PC side of things
Another way of doing it would be to have a radio (or maybe optical) beacon on the balloon and several ground stations that track it. You would be limited to line of sight, but that's how they used to do this sort of thing in the primitive days before GPS. I can envision a tracking station that monitored signal strength and moved the directional antennaback and forth to get the angle to the ballon. With several stations spaced far enough apart you can find the point at which the lines intersect. It would be very cool, but probably expensive and not very accurate (compared to GPS).