There are many different ways to track a high altitude balloon, and they all have their own pro's and con's. One of the more common methods is by using amateur radio and a protocol called APRS (Automatic Packet/Position Reporting System).
To track a balloon using APRS, first you need some form of APRS beaconing system onboard the balloon. The ArduinoTrack board is one such option, although there are many other ways to get a beacon. At minimum, a GPS receiver, a VHF transmitter (usually on 144.39MHz in the US), and some sort of computer interface between those two items. Also required would be some sort of power supply (normally a Lipo battery) and an antenna for the transmitter to connect to.
On the ground it can get a little more complicated. Many groups rely on the Internet gateways to see their balloons, and they use websites such as www.aprs.fi to see a map of the balloon and where it's been. This process is fine for use during the majority of the balloon flight, however when the balloon is on the ground, the Internet gateways won't necessarily be able to hear the balloon's reports, and consequently it will stop reporting.
To get around this, most tracking teams have at least one vehicle equipped with some form of APRS receiving equipment. This can be as simple as a handheld radio with built-in APRS capability (like a Yaesu FT-1D), or can be an elaborate tracking system that plugs into a laptop or tablet computer for chasing.