I got a used lamonde spin bike that comes with pedals that are cages on one side and cleats on the other side. I'm recovering from ACL surgery so I am looking to get more serious about cycling while I rehab my knee and can't do my sport for 8-12 months.

I don't understand how cleats work. Is it you buy the shoes and they basically have slots in the bottom and then you need to buy a pedal + cleat kit and install them on the shoe + bike? Is there any universal cleats or is it like you need to pick a brand and stick to it so everything fits together?