If you have DOD stickers and your ID, then you can get on base. The Pass and ID office should still be outside the base on Hampton Blvd. Following Hampton Blvd will take you right into the main gate. Also, off of that road will be the NEX.(Admiral Taussig Blvd which connects to I-564) Its almost the size of a Target, shouldn't be able to miss it on the right before the main gate.
I wouldn't worry about registering your car with NOB(Norfolk Operating Base) quite yet. If the rules are the same, you'll have to get a Va car inspection before you get NOB base stickers.(And it doesn't matter if you have another states plates, registration, license or insurace) This might have changed though.
The base has many entrances. Its the world's largest Navy base.

For now, I would stick with the main gate off of Hampton Blvd. (Thats if you're a carrier guy/gal....you can't miss the carriers at the far end of the base.....if you can't find them, leave the base and get your eyesight checked)
The sub base is kind of separate from NOB. I don't know a whole lot about that side. You will find out in the future that the airbase side has two gates and can be useful for working your way around during peak traffic times and making your life less painful if you have to go thru the HRB Tunnel. Hehehe......Norfolk traffic is something I will never ever miss.
In summary bring up Yahoo Maps and look at the base and find Hampton Blvd, follow that until you hit the Chesapeake Bay.

Have fun!