There are several ways to get into Twist Mountain: there's the entrance in the southwest part of Icirrus City, there's the basement in Clay Tunnel, or there's the original entrance from Route 7. I'm going to cover it starting from the Route 7 entrance. Even though it's the longest to get to, it is most familiar to players that have played the original Black and White games. Besides, that way you get to see Marshal again.
The Pokemon inside of Twist Mountain vary based on season. In fact, the entire mountain gets covered with snow during the Winter months, meaning you'll have to take an alternate route through it.
From the Route 7 entrance, head through the little tunnel until you reach the outside of Twist Mountain. Head north until you find the Red Shard, then head back to where you came in from except head south and east instead. Before entering the cave again, pick up the Float Stone just past the southern cave entrance.
Inside of the cave is a Worker who will fight you. He uses a Roggenrola L60, a Graveler L60, and an Excadrill L60. Continue just past him until there's a fork in the road leading north and another leading east. Go north and head outside to find a Veteran. He'll fight you in a Triple Battle and uses a Tauros L64 (left), Crobat L64 (middle), and Carracosta L64 (right). There's nothing outside aside from him, though. When you're done, go back inside and follow the past east, then north until you find another Veteran. She uses a Glaceon L63, a Bastiodon L63, a Drapion L63, and a Rhyperior L63. Keep going past her until you reach the outside part again.
Outside, follow the path north until you find a Hiker. He's got a Golett L61 and a Mamoswine L61. Past him is another entrance back into the mountain, so take that and then head east until you see the stairs. There's a Worker near the stairs that fights you with his Geodude L60, Steelix L60, and Boldore L60. Further east, past him, is a Dusk Stone for you to pick up. Otherwise head south and into the next room.
In the very bottom of the room, you can find a hidden Yellow Shard inside of a rock. Pick it up, then go fight the Worker that's running around. He uses a Machoke L61 and an Abomasnow L61. After taking him down, head outside, over to the west.
Head north to pick up the Full Restore and also fight the Nurse, who uses a Blissey L62, which gives a mountain of EXP when you knock it out. It has virtually no Defense, so use Physical-based attacks against it to take it out quickly. She'll heal your Pokemon up to full health afterwards, plus you can talk to her anytime in the future to heal up, too. Be sure to make use of that if you need some healing. Run around the side of the mountain until you reach an entrance going back in, but keep going before entering it to pick up TM91 (Flash Cannon), a Special-based Steel-type attack that has decent power.
Inside, head west until the first path heading north. Swing by up there to pick up a Rare Bone. Then, run over to the west back towards the start, following your Dowsing MCHN until you find a hidden Ultra Ball over near the side. Grab that, then head north until you find a Veteran. She'll fight you in a Rotation Battle! She uses a Gyarados L64, an Archeops L64, and a Kangaskhan L64. Electric- or Rock-type attacks are a good bet against her. Just past her is TM90 (Substitute), which is an interesting move that creates a decoy using 25% of the user's max HP. The decoy can't be affected by stat drops or status conditions, and it'll absorb damage until it breaks (after the foe does the 25% damage or more). It can be useful for setting up, but it is a little tricky to pull off. Head over to the east to reach the outside once again.
There's a Worker outside who uses a Sigilyph L62 on his team. Keep following the path until you see a door leading in; while there is another door to the east, it leads you to a dead end, so ignore it. Inside the cave, head north, ignoring the path directly to the east (it takes you to that dead end), and fight the Hiker. He has a Larvitar L61 and a Probopass L61. Take him down and then continue north, into another room in the cave. Down the stairs there, you'll find a Worker, and he uses a Glalie L61 and a Beartic L61. To the west of him is a Dusk Ball with another Rare Bone hiding in the rock beneath it. Heading south of the Worker instead will lead you to a door outside, taking you to the bottom of the exterior part of Twist Mountain.
Now that you're at the very bottom, pick up the hidden Full Restore in the trash can next to the bulldozer. East of that, you'll find steps leading down into the center part of the area, or a door over to the east. The door to the east leads you towards the actual exit of Twist Mountain, so start by checking out the basement.
Inside of the basement cave, you'll find a Worker picking away at the rocks. You can talk to him once a day to receive a random Fossil (or Old Amber). The only fossils he won't give you are the Cover Fossil and the Plume Fossil, which can be gotten from Lenora in Nacrene City instead. Definitely talk to him once a day to increase your collection of fossils. You can get them revived in Nacrene City, too, by talking to one of the receptionists in the Nacrene Museum.
Head east past the fossil guy and into the very basement of Twist Mountain. Here, you'll find a chilly stone that triggers the evolution of Eevee into Glaceon if it gains a level while down here. There's also TM71 (Stone Edge) waiting for you down here, which is a strong Rock-type attack with a high critical hit rate, but somewhat discouraging accuracy (80%). It's a good move, though. The southeastern side of the room leads you to Clay Tunnel, while the northern part of the room leads you to where you can find the sleeping giant, Regigigas.
In the room where Regigigas lies, you must first move some boulders out of the way. Head west until you reach the boulder. Use Strength and push it up all the way until it hits the wall. Wrap around and jump down the ledge so you can push it all the way to the east. Push it, then push the boulder over there south and into the hole. Now you can head over to the eastern part of the room, where there's another boulder. This one is a little trickier to direct, though. Push it up three times, so it stops one shy of being parallel with the nearby big rock, then push it to the west once, then up once, and then all the way to the west so it fills the hole over there, allowing you to proceed north.
Up there, you'll find the colossal Regigigas sleeping there. It won't awaken, though, unless you have Regirock, Regice, and Registeel in your party when you talk to it. You can get them from the Underground Ruins, but you'll need to either trade for one of them or swap keys with another version in order to get all three.
Its Slow Start ability halves its Attack and Speed for the first five turns of the battle, which helps counterbalance its overly high stats all around. It's a Normal-type Pokemon, so Fighting-type attacks are your best bet to do the most damage, but otherwise it is without resistances, so keep that in mind while weakening its HP.
Whether you catch Regigigas or not (or have to come back for it later), you can just walk south to return to the basement of Twist Mountain. Outside of Twist Mountain, head east on over to the cave you turned down earlier. Inside, you'll find a four-way branch by a Worker. The northern and eastern paths lead you to dead ends (unless you're playing in the Winter, of course), so instead just head the direction of the Worker to reach Icirrus City. You can talk to the Worker once a day to have him quiz you about construction stuff, and if you get five of his questions right, he'll reward you with a medal.
Well, now you've caught Regigigas, at least hopefully. That covers just another area you can visit throughout Unova after beating the game.