To begin with navigate to www.photobucket.com and click on 'Sign Up'
Sign up using either your details or Facebook/Twitter
Once you have signed up, and signed in, click on 'Upload'
Once you are on the upload screen click 'Select Photos and Videos'
Now browse to your photos, select the ones you wish to upload and click open
The selected images will then upload, and the screen below will be shown. Here you can click on your pictures to be taken to that pictures page.
Once you are on an image's page, you can copy the IMG code on the right, in most browsers a single click copies this link but you may have to select it all, right click and copy
Paste this IMG code into the forum thread reply box along with the text you wish to post
When you post the picture is shown
To copy more image links you can go 'Previous' and 'Next' on the image page on photobucket to go through your pictures.
You can also set up albums to organise your pictures, but do this before posting on here as your links may change.
You can view all pictures at once if you browse through your albums, and hovering over them also offers an IMG code to copy.
There are many more features, such as using it to generate multiple IMG code at once among others. Have a play around with it and you'll soon get used to it.
Other services are available, but photobucket is a good free one to use