First off you will need a Photobucket account.
Once your account is activated, you must first upload any picture you want to share.
Uploading to Photobucket
Firstly, click on the green 'Upload' button which is located at the top of the page towards the centre of the screen:
This will then take you to the next screen:
Hit the green 'select photos & videos button in the centre, then chose the content you wish to upload from your PC:
If you want to upload more than one image you can either hold down the CTRL key and select multiple images, or you can use Photobucket's bulk uploader which is available with an option on the screen
Adding images from Photobucket to the forum
Find the image you wish to display on the forum in the relevant album of your photobucket account.
Either hover your cursor over the thumbnail for the picture you want to put up until this box appears, then left click on the link I've highlighted. It will automatically copy it:
Or alternatively, left click on the thumbnail, then on the next screen right click the bottom option to copy it:
In both cases, come back to the thread you want to put the picture on, right click on the text entry area and choose 'paste' from the option box that appears or the "ctrl" & "v" keys together:
I find this easiest to do by having multiple browser tabs open.
I would personally advise altering the default settings on your Photobucket account so that your albums are all private. The option for this can be found if you hover over your Photobucket username and by clicking: 'Account settings' then by choosing the 'Privacy' tab. You'll still be able to share the images you wish to, but your images will not appear to those using search engines to search for images on the web.