Pokémon Emerald is in essence a 3rd R/S so many things are going to be the same in Emerald as they were in Ruby/Sapphire, however the way to get the Regi's is not one of them

First thing you do need to do is go to Route 134 as usual into the Diving Spot. Once in there, real the Braille on the far inscription and use Dig. The Door will open. Now here is the change, in that room go and read the Inscription. Now put Wailord First in your party and Relicanth last (it was reversed in RS) and read it again. An Earthquake will occur and the doors will open
First we will start with Regirock. His cave is in the south of the Desert so go there. When you get there, read the inscription and then go 2 Steps Left, 2 Steps down and then use Rock Smash. The Door Will Open and you can battle Regirock at the usual Lv. 40
Secondly we'll continue with Regice. His cave is in Route 105 so go there. When you get there, read the inscription and then do a clockwise lap of the cave, staying next to the walls at all times. Once you have done a full lap, The Door Will Open and you can battle Regice at the usual Lv. 40
And we'll end with Registeel. His cave is in Route 120 so go there. When you get there, read the inscription and then go to the middle of the room and use Flash. The Door Will Open and you can battle Registeel at the usual Lv. 40