As you approach Markarth, the capitol of The Reach, you'll want to make sure you take a left off from the main road- you'll find yourself in a small stone-homed village around the Left Hand Mine.  Left Hand Mine is of little note itself- while it is a rather productive iron mine (holding five ore veins that you can avail yourself of if you have the time and inclination) the real occurrence of note is going on as you enter the small mining town.

Two locals, by the names of Pavo Arturus and Gat Gro-Shargakh, have just entered town.  They previously were working at Kolskeggr Mine, due East of Markarth by the river, but that mine has been overrun by the Forsworn.  These two are the only ones still alive, the rest having been killed.  The local head of the Left Hand Mine, Skaggi, promises to send to the Jarl for some troops to clear Kolskeggr out- but if you've been to Markarth then you're aware that the official stance is that there are no Forsworn.

In the interest of seeing the problem brought to an end, you can then opt to talk to Pavo or Skaggi and offer to take care of the issue for them- Skaggi Scar-Face is willing to put up the two miners, but Kolskeggr is their home, and they'd much prefer to return there, as Left Hand Mine simply hasn't the work for them at the moment.

The Forsworn outside the mine are easy enough to take out- there are only three, and they like to patrol the bridge by Pavo's house, which is an easy place to pick them off with long-ranged attacks.  The path to the mine is behind the house- which is locked.  If you're apt for thievery you can take Pavo's stuff while he's gone, but none of it is really valuable enough to be worth the bounty.  Climb the hill behind the house and pass under the ruin arch to reach the mine, whose entrance is just left of the large black smelter.