How do I go about hanging a hammock?
This depends on your walls. Assuming your walls are the typical 2x4 studded drywall, fastening into studs is probably a bad idea; studs aren't designed to withstand that sort of horizontal load, and you'd likely damage the wall and structure over time.

An alternative might be to fasten hooks for your hammock from the wall's top plate. You'd need access above the wall in order to do this, but you could install the fastener pointing down, so that you are essentially adding to the load above the wall. Your wall is probably designed to support a load in that way, so adding a few hundred pounds shouldn't be a problem.

That does seem like quite a lot of work, though. Unless you're really sure you want this hammock to be a permanent feature of your room, it's probably less work (and definitely more flexible) to make or buy a stand. Search for "how to make a hammock stand"; there seem to be several good guides.