Nick's got it basically correct. The first step is to calculate the capacity you need, based on the load you anticipate.

You may be able to add additional receptacles to the existing circuit, it will depend on what else is already on that circuit, and figuring that out is a trial-and-error process. Plug a lamp into each receptacle in that room and adjacent rooms, next to and above/below the room you're concerned with, then find the breaker that controls the receptacle in question and see what else goes off when that breaker is turned off.

It's been a long time since I looked at the code, but when I rewired my early 1920s house years ago, there was a code-imposed limit on the number of receptacles or light fixtures you could have on a given circuit, regardless of the actual load (probably so you won't grossly overtax the circuit by plugging stuff into all of the receptacles.) I think it was, at the time, about 8 duplex receptacles per 15 amp circuit.

If you have the load available, you can just replace the existing junction box with a larger one. They have 3 and 4 gang boxes that are designed to free-mount in the wall without being attached to a stud, so you might just poke a hole next to the existing junction box, attach a piece of Romex cable of the correct gauge (14 gauge = 15 amp, 12 gauge = 20 amp) on the spare terminals on the existing receptacle, and bring it into the new box and attach to the first receptacle in the new box. Then, daisy chain the wire between receptacles in the box.

It's the same deal if you run a new line, except you have to, of course, fish the new cable down to the breaker box and install a new breaker. That's actually pretty simple, provided there's a master breaker where you can disconnect all power to the breaker box. Some older boxes don't have a master breaker.

Home Depot should have a book on basic home electrical work, and if you get one with illustrations, it really isn't rocket science. I would advise reading (either in the book or online) about the local electrical code so whatever you do is, in fact, done to code. Otherwise, as Tony said... you may be getting an unexpected visit from the fire department.