They knew an invasion would come, they just didn't know where and when.

The size of the operation was huge - it was the biggest sea/air invasion force ever seen.

Troops were trained without telling them what for - ok it was obvious it was for an invasion, but when and where was kept secret as late as possible. Workers that constructed the mulberry harbours were not told what the caissons were for. Those troops that would have a special mission (for example D company of the Oxford & Buckinghamshire Light Infantry who successfully captured pegasus bridge) were initially trained to simply "take a bridge", later on the exact layout of the Bénouville and Ranville bridges and the surrounding area was laid out with tape in fields and the plan of attack was drawn up and repeated incessantly, yet the men still didn't know where or when. A few days before D-Day all troops involved were confined to their camps and briefed on their exact roles. No-one was allowed to leave (although it is believed some slipped out through fences etc). Of course you couldn't hide the number of supplies, troops and vehicles (of all types) that were being amassed on the south coast of England - it was obvious to locals it would be soon.

Intelligence - Germany was at a disadvantage here. They had no genuine agents in the UK, they also had no photo reconnaissance to spot the build up. Enter Joan Pujol Garcia, otherwise known as Agent Garbo. A Spanish national he had a dislike for the suffering that war brang and on his own initiative he offered himself to the Germans as a spy, claiming he had business interests in England. This was all lies, in an apartment in Portugal he invented a imaginary ring of informants from all over England and created reports about life there and gave them to the Germans. He offered himself as a double agent to the British a total of three times, they sent him away. It was only when British intelligence discovered some of his reports (which were a little strange at times) did the British become interested. He was put under the control of MI5 and leading up to D-Day repeatedly told the Germans that the invasion would come in the Pas De Calais area (the piece of French coast closest to the UK). Even on the Morning of D-Day he was sending messages saying that the Normandy landings were a diversion tactic. His story is quite astounding.

Note that the RAF bombed a large area of the French coast to make it less obvious where the target landing area was - during this time for every bomb dropped on the Normandy landing zones they dropped three elsewhere.

Keeping the invasion area a secret was key - it forced the Germans to spread their resources more thinly across a wide area. Had they known where the invasion was to take place they would have concentrated their troops/tanks/artillery and it would have been a huge blood bath.

Had they known about the invasion the "Atlantic Wall" would have been much stronger. German propaganda had made much about the wall, but when Rommel took control of the area he was amazed to find in some places it barely existed and in other places was in no way sufficient. He immediately ordered that the defences be improved. If they had known about the invasion one would assume even more effort would have been put in to this, with the invasion area being even more heavily defended.