It is very doable, but not necessarily easy, and it sounds like you might not have the tools you need. You will need to pull the current freewheel, respace and redish the wheel, and put on a bmx freewheel. To do the respacing and -dishing right, you really need a truing stand.

That said, I've done this a lot (and my first time was on a Varsity!)and it's not hard. It is, however, time consuming. It might be cheaper and easier to buy a new 27" single-speed wheel.