It costs a good deal of money. Look on the website of any Beis Din.
The RCA website has their costs (google it). It ranges depending on the amount in controversy, but it ranges from 150 to 7500 in administrative fees, plus an hourly fee of 150 per side for a single dayan and 300 for 3 dayanim.
It is permitted for them to charge. Read the entire siman.
Also, you need to pay for your toen and your lawyer. You need both a toen to make the correct claims in beis din, as well as a lawyer to make sure you don’t do anything or say anything which will mess you up if you end up in the ?????? ????. I don’t know prices on this, but I can’t imagine it is less than 500 an hour for the two of those.
So you’re figuring at least 800 an hour during proceedings, and 500 an hour for outside work done.
(A get costs 500, on RCA website. I dunno what the lawyers charge.)