Yours is a little different than mine but if you don,t mind cutting the rubber hose off the top line that goes into the radiator all you will need is clamps and hose.
I cut the rubber off my top hard line with a tubing cutter then I attached the rubber hose and clamped it, now run that hose to the top of the cooler and clamp it.
Now run hose off the bottom of the cooler clamp it and connect it to the open line going back to the tranny. clamp it.
you can get all this stuff at the auto parts or hardware store except for your AN fittings which should have come with the kit.
Thats a mean ***** of a cooler, I looked at that one when I was shopping and decided it was WAY overkill but hey you got the best.

 

The mounting kit is 4 foam rubber squares, to keep the cooler a few inches off the radiator and 4 nylon pins that push through the radiator and have nylon squares with a hole in the center that hold them in place. Kind of like a zip tie that doesn't make a loop if you get my point. You should be able to find something like that somewhere.