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Depends on what kind, I mean, I can only help with game graphics. If you're trying to do like labels, or posters, or like graphic Ts, well I'm a poor designer when it comes to that sort of stuff.

So, what kind of graphics are you trying to get into and perhaps I can find something online to help.

The only thing I know it that in gimp you can 'export' layers to form a .gif, I think there is a free gif making program from microsoft that you can install - however it is terrible, I've tried it. There are also places online to compile gifs, but I think most cost money.

Gimp I do believe is free to use and download.

Edit:
Being basic here; When you want to make a gif you'll need several pictures, each one is change slightly or greatly depending on what you want the animation to look like, then they are placed on top of each other in the order you wish, and basically smashed together into a gif which shows one image at a time. Depending on the program or the amount of pictures depends on how fast the gif will change pictures.

Edit 2:
Since I've only done game graphics I'm more familiar with sprite sheets, it is the same steps making a picture over and over with a few changes, however I do not have to convert it into a gif, I merely hand it over to the coder who would then code the program to read each frame of the picture and set a frequency for the changes. (that goes for walking animation, attack animations, the program can be told when to change sheets, or what frame to start on in the sheet depending on the action the user takes or receives).