It's real easy. When you open a post here and want to insert a picture, you need to type brackets like this [i m g], followed immediately by the picture's URL, then another set of brackets like this[ /img ]. No spacing in between. I only added spacing within the brackets so the website wouldn't read it as me trying to insert a picture.
You get the picture's URL by pointing your cursor at the bottom left corner of your picture on photobucket to bring down a menu, then click "Share Links." When the next menu comes up, click "Direct" and that copies the URL. Go back to the forum and right click in between those brackets, then click "Paste." That's it. I hope I've described the process well enough that it helps.