This white sheet behind the insulation

Since you're going to have the walls open, I would use pre-faced fiberglass batting. The rolls give you more flexibility than the pre-cut batts if you have non-standard height walls and they're usually a little cheaper per square foot, but I see special offers in the big-box stores all the time so shop around.

There's no special trick to installing it, but wear a dust mask that's rated for fiberglass dust. The vapor barrier goes on the warm side. I usually cut pieces to length before installing them in the wall (but I'm an engineer and can't help myself! :), but you can cut it to size while it's in the wall if you're not as OCD as me: put the loose end at the top of the wall, unroll and stuff until you reach the bottom then cut it off. Run a bead of adhesive along the stud, then unfold the flaps at the edge of the insulation on one side of the stud and press into the adhesive. Repeat for the insulation on other side, then staple the two of them into the stud. Tap the staples in with a hammer if they didn't go all the way. Done!

I don't have a book recommendation, but it's easy to learn how to do it.

Does that insulation go into the ground? In otherwords, is that exterior insulation for the basement foundation? If so, then it's pretty much useless at this point. It wasn't sealed properly and is likely waterlogged and providing minimal insulating value. In which case, you can just get rid of it.

If, on the other hand, it's insulation on our exterior walls of the house, I'd suggest trimming off a bit of the bottom (you don't want that stuff in direct contact with surface concrete or soil). I'd then probably consider some sort of cedar skirting to match the siding and glue it onto the insulation (again, making sure the skirting is not in contact with the ground).