Succeeding in capturing Regirock is quite a feat - he's hard to find, and it's impossible to capture him until you've beaten the League and unlocked the Burdock Road. However, after unlocking the Burdock Route and gathering supplies (listed in the “Items Needed” section at the bottom of the article), you can start looking for this Pokémon.
Part 1 of 4: Entering the cave on Route Bardane
Step 1. Make sure you have gathered everything you need (see “What you need”)
Otherwise you won't be able to catch Regirock.
Step 2. Locate Route Bardane Route Bardane is a long, cave-like tunnel located northwest of Port Yoneuve
Again, this tunnel will only be accessible after defeating the Pokémon League.
Step 3. Go to Route Bardane
Again, you'll need a Pokémon that can use Surf.
Part 2 of 4: In the cave of the Route Bardane
Step 1. Head north after entering the cave, then go east at the first intersection
Talk to the NPC. You will access a new section of Route Bardane.
Step 2. Head south to the end of the rails
Then go west, then north.
Step 3. Continue north until you meet another NPC
Talk to him to go to the next section.
Step 4. Walk south, then go east at the corner and talk to the next NPC to continue
Then go south and then east again and talk to the new NPC.
Step 5. Head towards the blue basin
Use your Pokémon's Surf ability to navigate to the door and talk to the next NPC. This will unlock the door, go north and go through it. You will now be in the Buried Ruins.
Part 3 of 4: Into the Buried Ruins
Step 1. Go north, towards the big door, but don't enter
Stand in the center of the circle on the ground, then take six steps south and nine steps east.
Step 2. Turn your character so he's facing south, but don't take him one step further
You should find a hidden switch. The door will open.
Step 3. Go through this door
This will bring you to the Regirock room.
Part 4 of 4: In the Regirock Room
Step 1. Save your game
That way, if you fail for one reason or another, you can restart the fight.
Step 2. Talk to Regirock
This will start the fight.
Step 3. Decrease Regirock's HP
Start using Fire, Flying, Normal, and Poison type attacks. Regirock is a Rock-type Pokémon, so it will resist these attacks. In other words, it will greatly increase your chances of not knocking him out, which would end the fight.
Step 4. Capture Regirock
After you have sufficiently reduced Regirock's HP, try to capture him using your Balls. It is recommended to use Dark Ball. However, if you fail to capture it after 30 turns, consider using Chrono Balls. Chrono Balls are slightly more effective than Dark Balls, but to use them the fight must have lasted for at least 30 turns.