Originally Posted by Spoonrobot

You will just need a new rear wheel. You can get one for a decent price on eBay or VeloMine. You'll also need a cog and a lockring.

Now, you can just remove the freewheel from your current wheel and mount a cog. This is not recommended but has historical precedent. In this instance you will most likely rotafix the cog in place using loctite and make sure to mount both brakes. Get some foot retention and use both brakes to stop and you will most likely be fine.*



*I would not recommend it.

One more thing. That frame is generally accepted as a ladies style frame. So I hope you're either a girl or have the swag to pull off riding a girls bike.