As others said, you need one of those which will thread right on to your hub once you remove the old 7 speed freewheel using one of these if it has 4 slots around the axle:



If you have 2 slots around the axle, you need this:



Then, you will also need to respace your axle and redish the rim. That means that you have to take a spacer out of the side of the axle where that 7 speed cluster was and switch it over to the other side of the axle. Some rear wheels have multiple spacers in the axle that allow you to fiddle with the spacing. In any case, what is going to happen is that your rim will be moved over to the ride side (or drive chain side) of the bike. That will require you to redish the rim back to the left. Sometimes, you can get away with loosening all of the drive side spokes and tightening the non-drive side spokes.

Is your head spinning yet? This is generally not something the average person would be able to do successfully. You have to buy special tools and know how to fiddle with the axle and spokes. Then, at best, you might have a rear wheel that doesn't fail immediately because the spoke tension isn't correct. If you just ride around on the street, no jumping curbs, or otherwide abusing the wheel, it may be ok.

I second the recommendation just to use one of the cogs on the freewheel cluster and call it good.

If you want it nice, clean installation, get a single speed specific rear wheel. That is your most expensive option.

A mediium priced option would be to find a rear wheel with a cassette freehub body that allows you to use one of these:



You may be able to rummage around and find a good used wheel for $10-20. You can buy one of those cog and spacer kits for around $20.

Someone already posted a link to Sheldon Brown's singlespeed conversion how-to page. Good stuff there.