The Underground Ruins may appear relatively uninteresting at first glance — there's a wide open room with a large door leading into an empty cave — but if you solve the puzzle here, you'll unlock the Rock Peak Chamber and consequently either the Iron Chamber or Iceberg Chamber, depending on your version.
The puzzle is rather simple: at the back of the Underground Ruins, one of the statues tells you that you need to take X number of steps south from the eye and Y number of steps east of the eye in the main room. You'll see one of the numbers revealed during the AM hours (0:00-11:59) and another during the PM hours (12:00-23:59).
Thankfully, you don't actually have to wait around to find the directions out. You've got a walkthrough for that! From the very center of the eye in the main room (the "eye" being that double circle pattern), take six steps south and then nine steps east. As long as you are standing on that spot (doesn't matter where you're facing), press A and you'll find a hidden switch! Press the switch and then the large door will now lead you into the Rock Peak Chamber.
Rock Peak Chamber
Head to the very back of the Rock Peak Chamber to find a path leading you straight to the legendary Pokemon, Regirock! Make sure you save your game before trying to catch it, because you'll have to defeat the Elite Four and Champion again (with their levels much higher than before) in order to have another shot at catching it.
Dusk Balls are your best bet while trying to catch Regirock, at least until 10 turns have passed, when Timer Balls are an even wiser choice. It has extremely high Defense, so keep that in mind while trying to catch it!
After you've caught it, you'll unlock a special Key for the Key System. If you're playing Black 2, you'll unlock the Iron Key; if you're playing White 2, you'll unlock the Iceberg Key instead.
Save your game and then return to the main menu of the game by resetting. Go into Unova Link and then select Key System in order to change what's behind the door. You'll want to change the Mystery Door setting to the new chamber you just unlocked.
The Key to Completion
The Key you receive depends on which version you're playing, meaning you can only catch two of the Regi trio on a single version. If you have a friend that has your version's opposite (White 2 if you're playing Black 2, and vice versa), or if you have both versions and have unlocked both of those Keys, you can use the Send & Receive Keys feature to share Keys with your friend or other version. This unlocks the Mystery Door setting for the other version, allowing you to have a chance to catch both Regice and Registeel with some cooperation.
The Iron Chamber requires the Iron Key, which is unlocked only in Black 2; if you're playing White 2, you'll need to Send & Receive Keys with a player who has unlocked the Iron Key in their version.
Inside, you'll find Registeel!
Registeel is a Steel-type with high Defense and Special Defense. Whittling away its HP may take some time, so be ready for a long fight. It does have several weaknesses for you to take advantage of, though, including Fire-, Ground-, and Fighting-type attacks.
The Iceberg Chamber requires the Iceberg Key, which is unlocked only in White 2; if you're playing Black 2, you'll need to Send & Receive Keys with a player who has unlocked the Iceberg Key in their version.
Inside, you'll find Regice!
Regice has extremely high Special Defense, but it has many weaknesses: Fire-, Fighting-, Rock- and Steel-type attacks are all effective against it.
Whenever you're done, go ahead and lead the Underground Ruins and Clay Tunnel. Your next destination is Twist Mountain!