Sometimes, your Android phone is the best (or only) way to get your computer on the Internet. Since version 2.2, native tethering has been built into Android, and as long as the folks that made your phone or your carrier haven't removed it, it's a great way to get online. And it's easy, too!
Open the settings by tapping the menu button, then choosing Settings, Wireless & networks, then Tethering & portable hotspot. You'll see what's in the picture above, and have two choices here -- do it over a wire or turn your phone into a wireless hotspot. Just choosing "Portable Wi-Fi hotspot" will probably get you right up and running, but you'll be using an open and unsecured network. You can change the security method in "Portable Wi-Fi hotspot settings" to WPA2 PSK (a fancy way of saying you'll need a password to use my phone for Internet), and you really should. You can also change the network name if AndroidAP just doesn't do it for you. On a computer, you connect just like you would any other Wifi router.
If you plug your phone's USB connection into your computer, you'll also have the option to use it as a USB modem. This is even easier than using the hotspot feature, provided you have installed the drivers for your phone (see the forums for help with that). Just check the box, and your computer will configure itself to use your phone as a network device. I've tested this extensively on both Windows 7 and Linux, and often use it when I'm sitting somewhere out of range of my own wireless router. The bonus of using a USB connection is that it won't drain your battery -- it's plugged in!
Now we have to mention two things here -- these instructions stand for stock Android. Your phone may have things laid out a little differently for the USB modem settings, and may not even have these settings at all. And there's the fact that your carrier will likely want to charge you for tethering. We're not going to debate that issue, but we do want to advise you to check with your cell provider about any fees or restrictions before you try this one.