Simple man, just go to the picture you want on your photobucket and look on the right side for the IMG code. You can copy that text directly and paste it and the picture will work.
You can also post pictures by clicking the icon above the reply box that looks like a picture, you then paste the URL of the picture and it will post it for you. The first method does this for you by pre-tagging it.
I'm using Photobucket, and it doesn't seem that simple! Now, give me an Atari 2600 and I can work wonders...
Left click in the circled text and it will tell you that the link is copied. It not only is copied but has the image tags already added. All you have to do now is go to your reply window here on the forums and either press ctrl+v or right click and select paste. Your image will now be posted in your reply.