You have to book the train tickets ahead of time, the rest you can do the day of. You can book Perurail tickets online. You can also buy entrance tickets online, which they limit to 2500 per day (I believe).
I stayed in Ollantaytambo, which is cheaper than Cuzco and where the train to MP actually is. You just have to take a minibus or taxi from Cusco, the minibus is about 10 soles each way, the taxi will be more. This takes about 1 1/2 hrs from the center of Cusco.
I took Cruz del sur bus to cusco, but the people I spoke with that were flying said not to take Taca or LAN because they charge a fee if you book their cheapest fares.
MP, like much of Perú, is amazing.