When you start a game in Spelunky SD, a window will ask if you want to start a solo game, host a game, or join an existing game. To start the cooperative mode, just create a new game or have your friend do it, and then both join.
The gameplay in Spelunky SD is practically identical to the original. This means you have to try to get to the end of dungeons full of spikes, snakes, giant spiders, holes, and much more. And if you die, you have to start over from the beginning no matter where you were.
Spelunky SD is excellent news for Spelunky fans. It lets you keep enjoying this game, essentially the same as the original, but now with friends via the Internet.