The ambiguity of this is exciting! I'll take a stab.
First of all, I assume you mean the rear derailleur? is there a front or is this just a five speed?
Either way, the correct Huret original equipment replacement derailleur is available for free, or possibly the cost of shipping, from many forum members. All you must do is ask. This derailleur was made in the many millions and is nobody's favorite. You could also upgrade it to something period correct for almost no cost. Ask for more details.
If you /want/ a single speed, you have a couple of options:
The poor person's single speed uses one of the (or the) front chainring and uses just enough chain, after removing the rear derailleur, to wrap around one of the rear cogs. The drawback is that the chainline needs to be pretty straight--meaning that the plane of the chain needs to be parallel with the centerline of the bike, lest the chain derail itself under load. This means that you are stuck with whatever gear ratio gives you a straight chainline. Advantage: cheap. To complete this operation, you need: a chaintool (or a visit to the local bike shop (LBS); EDIT: and also some wrenches to remove the derailleur and wheel and so on). Here's an example:
The classier option is to purchase a single speed freewheel, which come in many different tooth counts, giving you a lot of different gear ratio options. In theory, the chainline can be an issue with this option without re-dishing the wheel (a involved operation involving adjusting all the spokes, best to be done by someone experienced, or someone paid to do it), but usually it works out pretty well. This is also pretty cheap, frankly. To complete this operation, you need: (1) to figure out what size freewheel you need and buy it; (2) the correct-standard freewheel tool (the freewheel with the 5(?) cogs screws onto the hub, but it can't be unscrewed without a special tool) or a visit to the LBS who will remove yours from your wheel for $5 or free; a chain tool (or a visit to the LBS). Frankly, this is also a pretty cheap option.
This is exactly the kind of thing that people do every day at the greasy local bike coop or in their garage or basement after reading how-to on http://sheldonbrown.com
. Ask if you want more help.
A chain tool looks like this (I have this kind and I love it--it doesn't let you push the pin out of the chain ...eh, you'll learn):
A single speed freewheel looks like this (note that the kid at your LBS may have no idea what this is, since the freehub, as opposed to freewheel, is the new standard for attaching spinny, ratcheting cogs to wheels):
A freewheel tool (not necessarily this one, there are several standards. EDIT: actually, this is the Atom freewheel tool, and your Varsity almost certainly has an Atom freewheel if that's the original rear wheel) looks like this: