You will need to already hold a private pilot certificate, since the instrument rating builds on top of it. Beyond that, under Part 61 you need to be able to read, speak, write, and understand English, pass a written knowledge test specific to instrument flying, and pass a practical test, the checkride, with an FAA examiner.
Good news on the medical front, you do not need a new one. The same medical certificate you hold for your private carries over. If you can fly now, you can start your instrument training now.