Naval and air superiority meant that the actual beaches themselves were usually pretty easy targets (with the exception of Omaha). So the allies didn't really encounter much resistance on the actual beaches, however as they began to advance out that is when the Germans began to put up resistance. The British moved forward from Sword beach they were counterattacked by the 21st Panzer division, the Panzer division did damage to the British mainly because the British tanks were trapped on the beach, but the Panzer division could do nothing and had to retreat for fear of being cut off. The Canadians advancing up from Juno beach were attacked by the 12th SS Panzer division, again the allies suffered heavy losses but the Canadians held fast and the Panzers retreated again. Hitler hadn't sent more reinforcements because he was convinced that the Normandy landings were a distraction and the true invasion would be in the Pas De Calais. When the Germans did begin to more men towards the Normandy beachheads, the allies bombed them constantly delaying their movements.

Source:

The Second World War: John Keegan