Does your bike have a cassette or freewheel? If cassette buy a spacer kit like this one.

Surly Single Speed Spacer Kit > Components > Drivetrain > Single Speed Cogs | Jenson USA

You will also need a cog. You can use one from the cassette you just took off or buy a single cog like this. Surly Single Speed Cog > Components > Drivetrain > Single Speed Cogs | Jenson USA

If freewheel, then you need something like this.

Shimano DX Single Speed Freewheel > Components > Drivetrain > Single Speed Cogs | Jenson USA. You will need to redish your rear wheel if you go this route.

If your bike has horizontal dropouts you don't need to purchase this next product. If vertical dropouts you need to buy some type of tensioner like this Surly Singleator Chain Tensioner > Components > Drivetrain > Chain Guides & Tensioners | Jenson USA

These are just a few of the products you can purchase. There are cheaper versions of all these, you have to decide how much you want to spend. You can also improvise by using PVC pipe as spacers, old cog from cassette and using your old derailleur for the tensioner. Without knowing the exact bike in question, it is more difficult to give you exactly what you need but this will get you started.