Basically, what you do is not post the pictures themselves to the forum, but only a link to it. If put into the [ img ] tag, it will also be displayed.
However, in either case you need to upload the picture itself to some web-space. This can sometimes be provided by your ISP, there are also some ad-supported offers for web-space on the internet.
To sumarize: The picture file hast to be physically present and accessible on the internet (your responsibility). The forum post only contains the link to it.