Give it a good soak in some water/vinegar mixture first. Gotta get all that crap off the new copper. You'll know it's done when it's shiny - 30-60 mins should do the trick.
I'd say just make sure you put it in the boiling wort for at least 5 minutes to sanitize it before you start. I just used my new one for the first time last week and it worked perfectly right out of the box!
Be careful with the hose that expels the water. I had a loose fit on the nozzle, readjusted it, and then turned it back on. The pressure caused the bottom hose to fly out of the sink and shoot water (200 degree water) all over my foot. The blisters were radical.
Triple check the hose clamps. I replaced my hoses before my last batch and the test run went good. I think the heat softened them up slightly and mine had a slow drip when i started the water. Needed just a little more to stop the drip once the hoses were up to temp.
+1. I never run my cold water into the chiller at full blast. Not only do I find it to be an inefficient waste of natural resources, I've also created two messy situations in which the hose popped off and sprayed water all over my kitchen.
I have found that the best pressure is one where you're sure you're optimally transferring temperature from the tap to the wort but not much more.
Pretty much what everyone has already said. I always test it before putting it in the wort. Put it in with 15 minutes left to sanitize it. After you put it in, check the fittings because the hoses will loosen up from the heat and you might get some leaks. Definitely watch out for the out end because it is out. Make sure something is holding the out end down because it might flow around at first with hot water and air pushing through the IC.
Before first use, clean it with water/vinegar or boil it well in water.