Two ways to get there:
First, Bus via Turbio to Natales (5-6 hours, around U$D 20). Night at Natales (U$D 10 plus food, remember not to take anything fresh, cheese, ham, etc. to Chile, they will confiscate it) and then bus to Paine (U$D 15; there is a new road under construction so it might be faster). Inside the park it could be another hour depending were you get down (inside TDP you could only move by bus or “dedo”, it’s to huge for walking).
It might be best for you to go by Cancha Carrera (Arg)/Cerro Castillo (Chile). There are some direct buses (ask at Calafate or Rio Gallegos) or you could take the bus to Rio Turbio, get down at cross road with Ruta 40, hitchhike the 6 Kms to the frontier, and once more bus or hitchhike from there to TDP. This would usually take not more than 6 hours and cost U$D 20.
The only problem I see with your question is that if you need to ask how much it could cost you -being such a great place as it is- Paine might not be the place for you. Anyhow, try to make it