Basically, you upload your screenshot as an image to one of the free image/photo hosters on the Internet. Then you link to this screenshot in your forum posting, using the "image" tag. The image hoster may offer a thumbnail, a smaller preview image, that expands to the full image once you click on it.
There are plenty of image hosters, I would go for one with no ads for the end user. I have used
http://photobucket.com in the past but there are many others. Some are listed here:
http://en.wikipedia.org/wiki/List_of_photo_sharing_websites.