I am in no way an expert - I can't keep 'impossible to kill' lucky bamboo alive in my house, but my mom used to have me help her repot her house plants, including aloe.

If your plant is root bound (ie has filled the pot to the edges with roots and they are weaving themselves along the sides of the pot), you probably want to go much bigger; otherwise a little bit bigger pot is fine. My mom uses whatever potting soil they have at the grocery store. There is also special cactus and succulent potting soil which has more of the non-dirt stuff they add for aeration - I don't know if it is actually worth paying more for or not. Cover the bottom of the pot with a layer of stones so that there is a place for the water to go if you over water your plant (just any old stones you can find outside.) If the plant is badly root bound, you want to shake out all the soil and roots and try to gently get it to un-ball up, otherwise you can just put the existing plant and any dirt that sticks to it into the new pot. Hold it up if you have to and gently add dirt to fill the pot. Water and fertilize (if the potting soil doesn't have fertilizer in it.) Adding fertilizer is optional but often a good idea when you repot (which is why potting soil often has fertilizer.) Good luck!

Thank you! That's exactly the kind of information I needed. :)

@competentgirl by name, competent by nature ;)