You go to a photo hosting service like
ImageShack® - Image Hosting,
Webshots - Photo Sharing, Free Wallpaper and Free Screensavers, or
Image hosting, free photo sharing & video sharing at Photobucket. You upload the pictures you want shown. Once it's finished uploading, it should give you the links to the picture. From there you have several options.
One option is to select the image formatted for forum and blogs, which will have the "[img][/img]" tags in it. You copy and paste that link into the reply to the thread and you're golden.
The other option is to select the direct link to picture, copy and paste it into the forum and then add the [img] tags. For example, if your picture is hosted on like www.thisismypicturehosting.com/picture.jpg
you copy the link and then make it look like [img]www.thisismypicturehosting.com/picture.jpg[/img]
The advantage to the direct link is that it won't show the annoying frames for photobucket or imageshack and stuff.
That simple.