First off, you will be going to Searing Gorge and a quick "flight" to Blackrock Depths. Once you get near the instance, you go up a "wooden slabbed" hill near where my cursor is. Once inside, follow the curve and just fly down toward the fire pit, and on your right you will see a little doorway, go in, maze a bit, then BAM! at the instance....
Once inside, there will be a doorway to your left. Enter through there. Immediately to your right (after going through the doorway), you will see another door.
Once again, you have another door to go into (on your left), but this isn't like the other "gates", this is a solid "steel" door. Go right in...You will see a set of stairs on your right. Two sets of stairs, go up em both. 
Once you get through the second staircase, you will see the "Ring". Run around the half circle to the highlighted doorway, then take an immediate right (there are a few packs of lvl 51-53 mobs before you see Pyromancer Loregrain, which is the "mini boss" that will drop your Formula: Enchant Weapon- Fiery Weapon.
If you see this, then you found him. Easy Peasy? Yup. He's at the back of the room. After you take care of business (and hopefully get the drop), then you can run out the way you came, get to the "Ring" again, and jump over the "lip". See the little door to the left there? Run through there, and take a sharp right.
When you get to the opening, the start of the instance is literally across the open space in front of you. Now you are done with "round one". Step outside the instance, do a "Reset all Instances" (right click your picture in the upper left of the screen, and there's a dropdown box). Now all you gotta do is this four more times, and then hit the AH with your recipe(s)!
If you are one of the lucky ones, you can get a few per run. If you are unlucky, well, you can walk away with just vendor blues from the boss (last night I was 1/5- didn't get screenies....this morning, 0/5). Now there are plenty other ways to farm in this instance, if you are interested, holler and I will do a total run through (but a warning, the other drops are not nearly worth the time or effort with current prices). Most of all, this isn't meant for a "UBER GOLD PER HOUR" spot, it's just a fun location that brings me back to my WoW "childhood".
*the post is a bit sloppy with all the pictures, hopefully it isn't too distracting...
Do you have an "old school" instance you like to farm here and there? Or a certain spot for soloing mobs that you frequent lately? Holler out, as I am always looking for new "soloists". If you don't feel like commenting, and are interested in turning it into a post, toss me an email at altosgoldishadvice@gmail.com
Xander had a great point as well in comments that needs to be met:
Hey just wanted to add in that there is a vendor inside the instances. Instead of turning left turn right and go to the npcs and look for Yuka Screwspigot the Engineering Supplys npc. You can sell your vendor trash and repair but all she sells and on the last page pick up the Schematic: Deadly Scope. and Fyi everytime you reset the instances it reappears. Sells for about 20g each if not more depending on how many people are farming BRD.