You would need to call or go down to the courthouse where the custody papers were filed. Ask to speak with the civil clerks and bring your case number if you have it handy. How immediately you could get the papers may depend upon how old the case is (the clerk may need to access storage in order to get and copy the records). Be prepared to pay a copying fee for the papers.
If you are expecting to modify custody, your lawyer would likely need a copy of the current order.
The papers would have been filed at the courthouse in the county where this took place. Check with the clerk's office to see if anything has in fact been filed. If so, they can pull your file for you to see what is there. If you are getting a lawyer - the lawyer can get this for you.