The main purpose of a tripod is to hold your camera still so you can shoot at a slow shutter speed and still capture a clear image. It is also used often for self portraits on holidays in my house.
You attach your camera to the tripod by screwing a little piece into the bottom of your camera. That piece then clips into the tripod. My tripod has lots of different adjustment options; ways it can swivel or pivot. There are also a couple of small levels - tubes of liquid with an air bubble in it - to help you know when your camera is sitting flat.
Tripods are also extremely helpful with self-portraits and group photos. Every holiday, my family sets up the tripod, gathers together in front of the fireplace and then I make sure everything looks good. I set the self-timer, press the shutter button and then run into my place in the lineup. If it weren't for a tripod, we wouldn't be able to have any group photos with all of us in it.
If you don't have access to an actual tripod, you can improvise and use the tops of tables, cars, tree stumps etc etc. The list goes on and on, but the principles are the same. You want a steady surface, and you want to eliminate your own shake. So use that self-timer and back away from the camera and tripod!