I've seen tin studs used in basements. The tin rails are set to floor with masonry nails. to ceiling with screws. And they use these things called tin snips to secure the vertical tin stud things inside the rails. Not like the scissor type, but it's a type of screw to secure tin studs to rails.
Also you'll need a plumb bob. You set the top first and then drop the plumb from both ends of one side. Then you have a location for the bottom. You'll also need some tin snips ( the actual snips/scissors ). But you won't need a miter saw so that's nice.
My vocab may be off, I'm not a contractor. Maybe the rails are called something else? I don't know.
To answer your q though, from what I've seen and read about it's a top and bottom thing, and then you put the vertical studs in between. This regardless of the type of material.
On some old houses I know they take a vertical 2x and make it so the widest width is apparent. In other words if you have a 2x4 and you want to secure it directly to the wall, you do so making sure the 3.5" of width is apparent. Then you can hammer nails (powered nail gun with masonry nails) or drill through (for lag bolt/shield, maybe tapcons.. not sure about this).
as far as shooting into the concrete, you might encounter some pitfalls. check out these two threads.
shooting treated 2x4s into concrete
shooting treated sill 2x4s into concrete