Which cords do I buy to hook up studio monitors to a audio interface
Powered monitors or passive?
Depends on what type outputs you have on the back of your interface. They'll either be rca, 1/4 inch or both! From there you go into the back of your monitors and they'll also be rca,1/4 inch or both. (some also have balanced inputs,three prong like microphone connections) and that cable would be XLR on female on one end and 1/4 inch on the other end that would come from the outputs of your interface. XLR connection is best if your monitors have them then 1/4 inch then rca.
If you have powered monitors with just those connections you should get sound. If they're passive monitors (unpowered) you'll need an amp to power the speakers or you'll get NO SOUND.
U may want to invest in a mixer as well to tie everything in together. Nothing fancy, something low cost will suffice til you can upgrade.