First, you will need to upload your image to an image hosting service such as Flickr, Smugmug, PhotoBucket or the like. I have my own website so I just use that.
After you have uploaded your image, the site can supply a sharing URL. This varies from site to site, but if you look for instructions on Sharing on that site you should be able to find out more information.
When creating your Reply here on the Boards, click on the little Picture icon (a mountain with a yellow background) and insert the URL you got from your image hosting site into the dialog box.
Preview your post and you should see your image in your reply.