I'll tackle the air superiority question on D-Day in two very simplified answers.

(Big Picture Answer)
1. We out-produced the Luftwaffe in both planes and pilots. But primarily the Germans were unable to replace their losses of trained and competent pilots. Over time, that seriously degraded their ability to mount effective defensive air operations.

(Immediate D-Day Answer)
2. We basically had everything that could fly and shoot in the air for the first several days and pretty much brute-forced the Germans out of the sky.
We did that by both keeping a large amount of air cover above our forces and by also attacking the Luftwaffe while they were still on the ground preventing many of them from getting airborne in the first place.

If you need more detail or have any follow up questions, send me an E-Mail and I'll post more here.

Ditto what Apache said (I'd add that the Allied bombing campaign in Germany, which began in 1943, tied up a significant portion of the Luftwaffe and contributed to their general inability to control the skies over Western Europe from mid-1944 to the end of the war).

As to the tanks, I've done a lot of studies (collegiate and otherwise) on the development of the tank and specifically on the deveopment of armored warfare doctrine. If you'd drop me an email, I'd be happy to point you towards the appropriate research materials.

Re: Tanks
Panzer Battles by F.W. Von Mellenthin
Attacks! by Erwin Rommel
I am trying to remember a book by an American tank commander, but not having any luck.
Nothing significant in tank combat happened after WWII except in the Arab-Israeli wars. I don't have any books on those wars.
I studied this stuff for quite awhile, but have concentrated mostly on first-person accounts and "real soldier" stories of combat. If I can find any better references, I'll post them.

follow-up on tanks. The best book I've read by an American is Brazen Chariots by Robert Crisp. Another WWII account. If you are interested in the technical stuff, email me and I'll see what I can answer.