first off, welcome!
second off, what year/model vehicle?
third off, the basic steps are; drain the fluid through the drain plug if you have one - then follow the next few steps, then unbolt the diff case cover (sometimes you will have to pry it off just a tad once the bolts are all removed) and drain it all or what is leftover after draining through the drain plug. While the diff is draining; clean the cover itself and the magnet on the cover you just removed with some brake cleaner, it will have small metal shavings attached that are normal (if you see any large chunks you should be alarmed). Spray cleaner inside the case and wipe out any remaining fluid. Depending on what vehicle you have you may or may not have a cork/paper gasket that must be scraped off - remove what you can by hand, then scrape the remains off of the cover and case with a razor/scraper. If you have a re-usable metal style gasket just set it aside while you are finishing cleaning the diff. Once everything is clean - replace the gasket, making sure it is flush and in the correct position on the diff case, then bolt the cover back on. When bolting the cover back on be sure to start the bolts by hand, and tighten the bolts down in a star-pattern. Open the fill-plug on the side/cover of the diff case and fill the diff up until it starts to overflow - then re-insert the plug and tighten it down. Re-check everything is tight and you are good to go! That is a general way to do it - pretty easy, but it gets stinky...