The entire complex/area on its own is free to walk around. The Ruhr museum has its own entrance prices that can be fouind easily if you google them, and of course the food and drinks at the restaurants are not for free as well. Have fun!
When we visited the site the entrance of the museum was for free during an open door even. Nevertheless the access rates for the museum should cost a couple of EUR. The industrial site is freely accessible where you can walk or hike.
I don't remember, you can check the internet, because there are some packages (if I'm not mistaken) for certain area or the whole area. Or just go to the main lobby for information, it's on upper floor with the long escalator, and from there you can decide it.
Get quick answers from Zollverein Coal Mine Industrial Complex in Essen staff and past visitors.