I've used Photobucket for a number of years, it's easy to use.
In the image below you can see the choices for Library, which is the page shown, and Upload. When you upload an image it will be stored in your library. When you hold the pointer in the upper right corner of a picture in the library an icon of a gear a menu will appear. One of the options is to Get Links, this will give you the options seen in the image below. Click on the type of link you want and it will be copied, right click in the forum and paste the image there.
Below is the way the link appears, most forums will accept this type or URL.
Some forums, like Bleeping Computer like to see it in the form seen below.
Edited by dc3, 17 August 2013 - 01:29 PM.