Super easy...
It's pretty straight forward. Just go to their site, click on the BIG green button that says Upload Files to MediaFire.
If you have an account, log into it. If you don't, you can create one (15 seconds is all it takes). Or if you're lazy, you can upload without an account (you just won't be able to manage any of your uploads later on).
From there, a pop-up of sorts should, well, pop-up and let you select the files from your computer that you wish to upload. Select the one(s) you want, then click on the Start Upload button to the right. If you have an account, you'll have to select a destination folder for your ** DEAD LINK REMOVED ** material.
Once the upload has finished, click on the share button and you'll be provided with three links. One for direct download (w/o filename), one for direct download (w/ filename), and one for website use (ie: html embed). Chose the one of the first two for forum use and just copy & paste it in the appropriate forum.
All in all, pretty simple and straight forward if you ask me.
Of course, with a little search of their site you can readily find many FAQs that should help you out with any further questions.
Edit: Oh, and be sure to provide screencaps and general info regarding the clip when you post it here...