The simplest kind of braid is called an English braid. This is the "regular" kind of braid, the one most people learn first. It's really a good idea to practice this one until it's easy for you before you try complicated braided hairstyles. It lets you learn the basic skills you need to make almost any kind of braid, and you can use English braids as the base for more elaborate styles.
When I haven't done it for awhile I always think to myself "bring the outside over into the middle" to remember it. That might make sense to you if you already know how to do it (or maybe I'm just wierd). For anyone just learning, I better explain it.
First you want to make a ponytail. (When you get better at it you can skip this part if you want.) If your hair is really long you could make it at the back of your neck. Usually you want the ponytail higher up, like the height of the tops of your ears, and in the center of your head so you can reach it with both hands easily. Use a simple hair elastic to hold it. Later on you might want to use a fancy scrunchie sometimes but when you're learning it will just get in the way.
Separate the ponytail into three strands. Don't worry too much if the strands aren't exactly equal. It'll come naturally after you practice enough to figure out which finger movements work best for you. Some books try to tell you how to place your fingers at every step, and maybe that works for some people. For me it works best to just close my eyes and go by feel. Either way, only practice will let you learn to control where all three strands are going. You can probably guess why: three strands, and only two hands.
Now comes the tricky part. Once you learn this next part, you just need to do it over and over again until you reach the end of your braid.
You have three strands of hair, with one hand holding two strands. One of those is the middle strand. Use your other hand to pass the "lone" strand over the middle strand, but don't let go. Use the same hand to take hold of the middle strand, so you are now holding two strands in the hand that was holding just one. The one that used to be alone is now the middle strand, and the third one is the new "lone" strand. Then cross the new lone strand over the new middle strand, and repeat the steps from there.
At first you might think it's much easier to say than do, but it doesn't take much practice to get good at it. Before long, the steps are so automatic you can do them almost without thinking about them. Maybe that's why most of what happens in so many beauty salons is conversation.
When you get to the end of the hair you want to braid, you can just fasten the end with another elastic. You might need to use a smaller one here.
After you get good at making this braid, there are all kinds of uses for it. You can use barrettes and other decorations in it, or you can braid a ribbon right into it. You can get another whole different look just by making more than one braid.
Don't let the simpleness of this style fool you. Sure, it's one of the first hairstyles little girls wear, but it can still be done up fancy enough to look right at home with a wedding dress.