What is tethering? Besides the grounds for a giant debate about ethics (the kind that you can only find on the Internet) tethering, in this case, means to share the Internet connection from your phone with other devices. There are several ways to accomplish this -- connecting your phone to your computer via USB, setting up your phone as a wireless hotspot and router, and sharing a data stream over Bluetooth. All these connection types are built into Android, with native Bluetooth tethering new in Ice Cream Sandwich. Of course, different manufacturers can, and have, modified things so that these options are excluded -- at the behest of the carrier, of course. We'll talk more about why in a few minutes.
Tethering itself is pretty easily done. USB tethering involves installing device drivers (Windows only) and plugging in your phone to a high-speed USB port on your computer, then using your computer's built-in connection manager to use the phone or tablet as a USB modem. Bluetooth tethering will need the phone paired with the computer, and the connection type set up correctly in your computer's Bluetooth settings. Wifi is the easiest way -- you just turn it on and connect as you would any other wireless hotspot.
Except that many carriers, especially in the United States, have blocked tethering this way.
You see, your carrier wants to charge you a premium to use your data plan from any device besides your phone. Nobody likes it, but it's in the terms you agreed to when you signed up. They have all sorts of ways to block tethering on their end, and they are pretty diligent about it. Android hackers and developers also have found ways to work around these blocks, and it's a big cat and mouse game. An inside source with one the the biggest cellular carriers in the world has specifically told me that if your usage pattern draws suspicion, there is no current method that can't be detected by you carrier, including the newer VPN methods. If you do it a lot, without paying the extra fees associated with it, you'll get caught.
We're not going to judge anyone, and a few of us here at Android Central think charging extra for tethering is silly -- especially with data caps. Just know what may happen before you start so you don't get caught unaware.
Previously on Android A to Z: What is sideloading?; Find more in the Android Dictionary