Glad to hear that you’re experimenting with your Macintosh, learning how to take screen shots and explore some of its many capabilities. I use a commercial application called Snapz Pro X for screen shots, but it’s darn easy to just use the software included with Mac OS X. For example, try pressing Cmd-Shift-3 to take a full-screen screenshot, or, if you want to select a specific region of the screen, use Cmd-Shift-4.
The Grab application (which you can find in Applications –> Utilities) makes this a bit easier, fortunately, but what you want to do is make sure that instead of you having the images in your copy/paste buffer, you always save them as graphical images on your Desktop.
Remember, you can capture all sorts of objects with Grab by using the “Capture” menu:

The problem is, Grab saves everything in TIFF format, which is incompatible with most forum sites, so you need to convert these to PNG, JPG or GIF format. How to do so? Open the TIFF image you’ve saved in Preview and “Save As…” a different format. I suggest PNG as the best option.

Now you should have your screen capture saved as a Web-friendly image and we can talk about the forum side of things.
Images on your computer need to be stored on a server somewhere on the Internet for other people to be able to see them (which is good: you don’t want anyone on the Internet being able to see what’s on your computer!) so you need to upload the image somewhere.
On most Forum sites, if they support you including images they’ll have an upload capability which might look as simple as a little image button or a small “upload” link. Find and select your image from your computer and it should not only be saved on the Forum system, but the necessary code sequence should be added to your forum entry so that when you save it, the image appears, as if by magic!
If you still can’t figure it out, email the forum administrator, asking for help. They should be happy to clarify things!