Start off by plucking or cutting one of the 'leaves' off of the main plant, dip it in your rooting compound (optional) and place it in your pot filled with potting soil. Simple as that.
After about a 1-2 months your cuttings roots should look similar to the ones above. (Time varies by plant.) I would recommend waiting another 1-2 months before you plant them in there permeant spot.
Cuttings may not always work well with some succulents, including aloes. But they may propagate themselves, naturally. That's how the aloe above was propagated.
Also with 'Hens & Chicks' (above) you can clip off one of the surrounding plants and put it in a pot once the roots get large enough. It will basically propagate its self, too.
This is the 'main plant' that I got the cuttings from back on the first page.