Section 1 - Basic Filled Circles, Squares (or similar)
Making filled shapes such as a square, rectangle, circle or ellipse can be done in a couple of steps.
1. Grab your rectangular selection tool.
2. Drag your mouse cursor on the image canvas to drag out a rectangular selection.
3. If you hold down shift while dragging out the selection, you can constrain the selection to a square.
4. Now, grab the bucket fill tool
5. Select a custom foreground colour from the colour picker in the toolbox and select "FG Color Fill" from the options dialog for the bucket fill tool (double click on the tool icon in the toolbox if you can't find the tool options dialog window)
6. Clicking inside the selection you have created will then make a nice square or retangle filled shape for you.
7. This process can be repeated using the elliptical selection tool to make circles and ellipses. Not surprisingly, holding down shift makes the elliptical selection snap to a circle.
Section 2 - Outlined Shapes
The next step from a filled shape is an outlined shape. Making outlined shapes follows on from the previous method.
1. Make sure you have followed all the steps in Section 1 above to create a filled selection. Make sure the selection is still active (ie - the marching selection outline is still showing).
2. On the right click image menu, choose select --> shrink.
3. Enter the amount of pixels you want the thickness of the outline to be.
4. Finally, clear (edit --> clear, ctrl+k by default) the now shrunk selection.
5. What is now left is a nice outlined shape. This same technique can be applied to any selection you can get your hand on, as shown in the second image to the left (I got carried away evidently).
Section 3 - Triangles, random polygons etc
There are automated scripts to make a variety of shapes*, but that is no fun now is it? Also, the "gfig" plugin available in the right click menu under filters-->render-->gfig may prove of assistance to you. However, an entire separate tutorial can be written about gfig. There are also plenty of disadvantages to using gfig, which I won't detail here (to the annoyance of gfig lovers everywhere).
I will however provide you with a couple of other solutions to making simple shapes which uses the path tool. If you don't know how to use the new path tool's features yet, please read the relevant gimp help file before trying the steps below. This will prevent you from breaking your mouse into 7 pieces.
1. Grab your paths tool.
2. Turn on a grid from the right click menu at "view --> show grid."
3. Under "image --> configure grid" you can set your grid to display how you like it. I like dots, you may like intersections. Each to their own. Depending on how precise you want your grid, you can change the distance between the points.
4. To make some good use of your grid for making geometric shapes, on your right click menu select "view --> snap to grid"
5. Now the fun starts. Using your pen tool space out three points as in the top-left of the image to the left.
6. To close your path, hold down ctrl and click on the first point you made. The path should close like the second image in the guide to your left.
7. To make an outlined shape from your path, using gimp's in-built stroke (line painting) feature usually provides a high quality solution. To access the stroke function, go to the paths dialog box and click the "stroke path" button
8. A window not dissimilar to the second image to the left will pop up, which you can use to select your stroke options. The options I used are shown in the screenshot. Feel free to play with these settings to mix up the effects.
9. If you would rather a filled selection, in the paths dialog box, select your path from the list and click on the "path to selection" button
10. A selection like back in Section 1 of this tutorial will appear, and you can use the bucket fill tool to fill the shape.
11. Some of my testing on shapes is shown in the bottom image to the left of this text. And people say gimp isn't suitable for making shapes!
* - please see http://registry.gimp.org to download such scripts or plugins.
Always remember if you're going to use extensive amount of effects and colors, and you're going to use this for your site, try optimizing the file size by using converting the image into index colors by going to Image > Mode > Indexed. Or if you want, you can also get dedicated server hosting to lessen the server load.