1: Go to www.Photobucket.com and register for a free account. Yes, there are a lot of annoying ads.
2: Upload your photo(s).
3: While viewing your personal Photobucket library, when you click on a photo, the necessary HTML reference code will populate in a text window for you to copy. So, copy that.
4: In the body of your response on Freerepublic, paste the code you copied from Photobucket.
Example:
The code from Photobucket includes a hyperlink back to the site. I routinely strip that out when posting here, so the end result is just the photo, like this:
I hope this helps.