That is, would they have had any prior combat experience to the Normandy Invasion? Did they try to use an army primarily of veterans from the Pacific/African fronts, or would D-Day have been the majority of the invaders' first day in the combat zone? In which case, were there any serious objections raised about sending green troops up against the presumably battle-hardened Wehrmacht?
I ask "American" specifically because I assume the majority of the British army would have fought elsewhere in the war (if only because of its smaller size), but the question could equally apply to them.
So, the American forces landing on Normandy on the first day of the invasion were (primarily) the 4th Infantry Division at Utah and the 1st Infantry Division and the 29th Infantry Division at Omaha. Of these, the 1st had seen a great deal of action, in both North Africa and in Sicily; the 4th, however, was fresh from the United States, and the 29th was actually a National Guard unit (from Maryland/Virginia). As Omaha was expected to be a tougher landing zone, elements of two divisions were detailed there, with the expectation being that the veterans of the 1st would help make up for the relative inexperience of the 29th. Also, a word should be said for the paratroopers of the 82nd and 101st divisions; despite similarly being largely untested, they too were still entrusted with high responsibility missions, and performed admirably despite pre-invasion plans being largely rendered moot by factors such as poor drop locations, officer casualties, and some poor intel.
As for the Wehrmacht defenders, a big part of the reason why Operation Overlord went forward was because Allied intel (mostly correctly) believed that the defenders on the beaches were 2nd- or 3rd-rate units, comprised largely of old men, boys, and conscripts. Allied planners believed that their fresh, well-trained soldiers would be able to overcome the beach obstacles with such poor troops opposing them, and they were largely correct. Of course there were reservations, but by and large the untested American troops performed extremely well in their roles.
For more reading, both of the two most well-known compendiums of the Normandy invasions - The Longest Day, by Cornelius Ryan, and D-Day, by Stephen Ambrose, discuss the training and order-of-battle of both sides fairly well, along with first-hand quotes from the soldiers who went through it. These both should be readily obtainable. You could also look at the biographies/memoirs of Allied leaders, such as Bradley and Eisenhower, in which the planning for Overlord takes a large role.