I'm mounting these against a basement wall. My basement is mostly dry, but I didn't want to hang things directly from the wall. What I decided to do was to mount 2x2 uprights of pressure-treated lumber, and to hang the cleats from that. This way, only the pressure-treated uprights would be in direct contact with the wall.
I mounted the uprights with Tapcon Concrete screws. For these, you'll need a hammer drill. For them to work, you need to remove the dust from the hole, after you've drilled it. You can do this with compressed air, if you have a compressor in your shop. You can do it with a shop vac, if you have one. I don't have a compressor, and my shop vac was buried under all the stuff I'd moved out of the way to make room for this project. But I'm a computer geek, mostly, and I always have cans of air, lying around. Worked just fine.
Drill one hole, then check for level then screw in a second.
My cleats are 48" and 96" in length, so I wanted my uprights to be 16" apart - except for the two ends, which I wanted inset by half the width of my uprights. The idea is that the ends of each cleat would be flush with the edges of the outside uprights, but the butt joints where the two cleats in each row would meet would be centered on an upright.
So, position the second upright, drive one screw. Either check for level, or check for parallel with the first, and drill a second hole.
Do the same for the third upright. For the fourth upright, use one of your four-foot cleats to make sure that the joint will be centered on the upright. The last upright should be flush with the ends of the cleats.
After I had everything fixed to the wall, I went back and added four more screws to each upright. That may be overfill, but I've always thought that anything that might be climbed on should hold the weight of two 10-year-olds.
I painted and primed, then proceeded to mount the cleats, using clamps to hold them in position while I checked for level.
I was about half-way through, when I realized that if I wanted to mount some electrical outlets on this wall, I should do it now.