First, you'll need to acquire the Black Pass from the Caging Tower, which sadly means this will be two-thirds of the game through. However, once you've acquired it, head to Little Twister and then go to one of the smaller houses near the back. This will allow you to walk around the back side of the town, where a lone hut can be found. The stairs in here lead down to the Black Market, which will require you to use the Black Pass at the door every time you enter it. You can either, at the point of entering, buy a Warp Star or Dragon Fossil for anywhere from 1000 to 2000, or return here for very specific purposes later.
The beauty of the Black Market lies in two things.
1) If you obtain the Gold Pass from the optional boss Heimdall Gazzo within the Dissection Facility, you can cut the prices in half for anything in the Black Market. This will make the EX File Key affordable.
2) You can sell Ailment-Ward and Element-Ward accessories to shopkeepers in order to buy an unlimited amount from the Black Market. For the later parts of the game, this is much simpler than trying to get them to spawn off of some fights.