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I run a number of games both online and offline and it's absolutely possible. Play by post games are almost built on that concept. I will say outright that visual aides are nice, just as props are with in person games. They're just easier to do online so most people use them; however, this does not make them a requirement.
As far as any advice on the subject goes, describing it online is going to be very similar to describing it in person with the obvious exception of body language, so you lose out on the ability to gesture.
There's a site called The Alexandrian that does a great job on going over Game Mastering tips and trick, and while that site is my personal favorite, there are many other great table top resources like that.
Another good thing to look into is the style of presentation for the narration of audio books, or the narrator's role in radio plays.
As far as using hand drawn maps, as long as you're clear on your markings of walls, doors, etc. anything should work fine, even just basic line drawings.