I always recommend more than one day. That being the case, you can certainly see some key sights if you have a car. Although I will add that to appreciate the sights, do your homework ahead of time, so you know the history and lay of the land. Reading books and researching online won't cost you valuable vacation days, but will immensely improve your appreciation of what you will see.
I'm going to make the assumption that you are American and hence are more interested in the American areas of D-day. As such, here are some key "must sees:"
The American Normandy Cemetery. It overlooks Omaha Beach, and has a wonderful, if sobering visitors' center.
Omaha Beach. Drive the length from Vierville-sur-Mar West as far as the road will take you. Walk out as far as the tides will allow, and look back to try to imagine what those debarking on this beach had to overcome. Again, very sobering—even more so if you read up on the battle ahead of time. In Vierville-sue-Mer, there is a wonderful little restaurant/hotel called Hôtel-du-Casino. Form their deck, you can enjoy a bite and look out over the deadliest section of Omaha Beach.
Point-du-Hoc. Again, the more you know ahead of time, the more you will appreciate this place where U.S. Rangers scaled a sheer cliff to assault and take a German gun emplacement.
Longues-sur-Mer. A German gun emplacement on a huge bluff overlooking the coast, including a couple of beaches of D-day. This will give you an appreciation of what the Allies faced when trying to liberate the immediate beach area.
Arromanches. This was "Gold Beach," which was an area of British assault. But after D-day it was transformed into a man-made harbor where tons of men and material were brought ashore in the weeks following D-day. You can wander the beach and see the remains of this harbor right on the beach, and off in the distant ocean.
You could see all of these things in a very busy day, and it will be very memorable. If I had one day, I would forego visiting a museum. Much of what you will learn from them you can learn ahead of time. And you're better of seeing the real sights in such a limited time. Having just one day, you will unfortunately have to give up many other sights such as Utah Beach (the best museum in the area IMHO), Sainte-Mère-Église (center of the U.S. Airborne operations), other cemeteries (British, Canadian, German, etc.), Pegasus Bridge, La Fiére Causeway, and many others. But hopefully you will find a way to return. I went once to "check it off my list" in 2008. I have returned six times since (5 on the anniversary of D-day), and will be there this June for the 75th anniversary of D-day.