Assuming the rings are removable (on some they're riveted rather than bolted), it's as easy as buying a new ring with the correct BCD (bolt circle diameter), undoing 5 bolts, remove old ring, fit new ring, do bolts back up. In addition to this, your front derailleur may need moving up a small amount.
However, most common ring sizes only go up to 52 or 53, so you may not find much of an increase. How many teeth does the smallest sprocket have on the rear? It may be easier to gain a higher gear ratio there.
Edit: Cross posted with Ian. I didn't consider the gap between the two rings that Ian did, so that's also something to keep in mind.