Saki.... such a conversion is one of the easiest things you can do.... and it's one of the best. That frame is great.
Harris Cyclery has a whole series of web pages devoted to converting bikes to single speeds or fixies, and they have all of the pieces you'll need. Basically, all you need to do is swap out your freewheel cassette for a single sprocket, remove the deraillieur, and shorten the chain. In the real world though, there's a little more to it.
First, there are 3 types of set-ups you can build 1-a fixie where the rear sprocket is fixed to the back wheel so that there is no freewheel, which means you cannot coast without pedalling. 2- a single sprocket freewheel where you CAN coast and 3- a coaster brake which works just like the cruiser bike wheel. The choice is yours, but from experience I can tell you that you'll be better served with options 2 or 3, and NOT with a fixed gear. They are a first class pain in the backside to ride.
My personal preference is for a Coaster Brake..... and Harris Cyclery sells a 27" coaster brake rear wheel that will fit your bike perfectly. It's pretty inexpensive, and makes for a very clean looking set-up.