Transparency
You should know what this is. If you don't... Well, I'll explain it. Transparency is kind of like see through. The area that's transparent will be the color of whatever is behind it.
Example:
How To
Please note, this tutorial is for GIMP.
First... Get an image. This page will basically tell you how to add transparency. So like, this will tell you how to make a sprite transparent. In other words, how to make your white background transparent. Okay. I know I'm boring you with all of those words, so lets get to it.
Here is the image/sprite that I'm going to add transparency to:
Now, open it up with GIMP (... duh). Then, click on Layer>Transparency>Add Alpha Channel. Then, select the wand tool. It's on the right of the lasso tool. On the tool options, make sure the threshold is set to 0. Threshold is explained below. After that, click on the area that you want transparent, in my case, the white in the background. Once the area is selected, click on Edit>Clear, or your hot key for Clear. That area should then have a gray checkered background. This means it's transparent. Continue to do this to all the other areas that you want transparent.
In the end, it should look like this:
Threshold
There is a little thing called threshold. It helps to make the image look better transparent. When you're using images that have the outline like the line on the right on the image below, make sure the threshold is set to 0. If you're using images that have an outline like the one on the left of the image below, you change the threshold. I'll show you what I mean.
The one on the left is a faded line, the one on the right is not. Sprites usually have an outline like the right one:
Hopefully you can see the difference...
Anyway, so you should leave the threshold at 0 if you're making an image that has an outline like the line on the right of the image transparent. If you're using an image with an outline like the line on the left of the above image, move the threshold around. To change the threshold, select the wand tool. On the options for that tool, there is a threshold slider. All the way to the left is 0. All the way to the right is 255. Don't put the threshold all the way to the right, or else it will select the whole image when you click. By moving it the the right spot, you can make the transparent areas look more clean and fit.