From Driftveil City, you can head down the steps to the west of the Gym to enter Clay Tunnel.
Inside, you'll find a whole ton of rail cart tracks. A Hiker is near the entrance, and he'll fight you with his Aron L61 and a Mawile L61. If you have a Pokemon with Rock Smash learned, you can head to the north to clear some rocks and fight a Worker. On your way, there's a Red Shard hidden in one of the rocks, so use your Dowsing MCHN to find it. There's also an Escape Rope hidden in the pit near the Worker. The Worker uses a Sableye L61 and a Dugtrio L61.
If one of your Pokemon knows Rock Smash, you can talk to the nearby Workers to clear the rocks blocking your path. However, this is not necessary, as you can just take the mine cart back near the start. I'll take you that route, so head back to the Hiker and then head northeast instead. The Worker there will offer to let you ride his mine cart.
Taking the mine cart will lead you over by a boulder you can move with Strength. Go ahead and push that into the hole, although head south so you can find where you would have entered had you used Rock Smash (if you don't want extra items, just skip ahead two paragraphs or so and cross the boulder). Along the way, pick up the Red Shard and fight the Hiker. The Hiker uses a Swoobat L61 and a Golem L61. As you can see, just past him is where the rocks are; if you broke them earlier, that's where you'd appear, so it isn't a significant shortcut really.
Head west until you see the rails branch north. There's a hidden Water Stone in one of the rocks in the area. Definitely pick that up! Push a boulder to the south of that to gain access to an HP Up and a Nugget.
Go back to the north and fight the Worker. He's got a Diglett L61 and a Machamp L61. On a little island to the east of him, in the middle of the water, is a hidden Steel Gem. Head north of that until you find the boulder from earlier that you pushed into the hole. It just wraps around the lake and provides a shortcut, but you would have missed out on items and Trainers had you taken it.
To the north, you'll find another Worker, as well as a fork in the road. The Worker uses an Excadrill L60, a Nidoking L60, and a Rhydon L60. The tunnel to the west of him leads to the Mistralton Cave, although if you checked it out earlier, there won't be anything new for you to see there, so head north instead.
In the other room, keep going north until you find a PKMN Ranger. He uses a Forretress L62, a Crustle L62, and an Armaldo L62. He'll give you a Lum Berry after beating him. Just to the west of him is a Metal Coat, which raises the power of Pokemon's Steel-type attacks by 20%, plus it evolves Scyther into Scizor and Onix into Steelix when traded.
Keep following the path to the north of the PKMN Ranger until you find a Worker. He uses an Onix L60, a Graveler L60, and a Steelix L60. North of him is a Max Revive along with another Worker, this one using a Graveler L60, a Golem L60, and an Onix L60.
There's nothing to do to the east for now (you'll have to move a boulder from the other side), so head north instead. That'll lead you to another fork in the road. To the north is a PKMN Ranger itching to battle, and she's got a Ferrothorn L62, a Cradily L62, and a Carnivine L62. She'll give you a Lum Berry after beating her. To the north of her is an entrance to the basement of Twist Mountain; you can feel free to head there, although that will be covered in a separate page of the walkthrough.
Instead, head east of the PKMN Ranger and talk to the Worker by the mine cart. Take the mine cart to a closed off portion of the tunnel. Head south and push the boulder into the pit to allow for a shortcut to get back here, plus it gives you access to a Rare Bone to the southeast. Pick that up quick and then go back to the other boulder. Push that into the pit, pick up the Green Shard, then talk to the next Worker to continue your ride through the tunnel.
The next Worker just leads you to a small area with a track leading down to another one. Nothing else exciting. Take the next mine cart. It'll take you over to a lake. Go on and Surf across that until you reach another tunnel, though pick up the hidden Iron before entering.
Push the boulder into the pit and have the Worker take you on another mine cart ride. Push the boulder you come across to the west into the pit, but then head to the north instead. Be sure to pick up the hidden Big Nugget hiding in the nearby rock, though, and then head into the tunnel, leading you into the Underground Ruins!