Neither the Allies nor the Germans employed a great variety of vehicles at the beach on D-Day. The Allies had to secure the beachhead as quickly as possible in Normandy, which combined with the aquatic nature of the landing, precluded the landing of most tanks and other vehicles until after the actual battle. In the instances where tanks were landed, the results were often disastrous. The Germans also did not have a great deal of armor or other vehicles present because the closest mechanized battle group was not actually deployed at the beach.
Most of the American infantry were equipped with the M1 Garand. It was the precursor to the modern assault rifle in that it allowed semi-automatic fire coupled with an automatic ejection of the eight-round magazine when empty. (If you ever watch American movies of the Second World War, you will often hear the magazine ejecting to its telltale "ping" sound.) Most British and Canadian infantry were equipped with the Lee-Enfield .303, which was a magazine-fed bolt-action rifle that held ten rounds. Although it was eclipsed in rate of fire by newer weapons, such as the M1 Garand, it was still an accurate rifle that fired an incredibly lethal round. In the hands of well-trained troops (see, e.g., the First Battle of the Marne in the First World War) it was an excellent weapon.
Another common weapon of the Allies was the Thompson Submachine Gun. Nicknamed the "Chicago Typewriter" from its popular use a gangster's weapon during Prohibition, it fired a .45 caliber pistol round in twenty and thirty-round magazines. This was larger than the 9mm round used by the SMGs of most other contemporary armies, making it more lethal. The Thompson also boasted an incredibly high rate of fire. While incredibly lethal at close range, the Thompson was a notoriously inaccurate weapon. I recall hearing one veteran saying it was only useful if you needed to clean Germans out of a closet. On the British and Canadians sectors of Normandy Beach, their infantrymen were also using the Sten. The Sten was made entirely of metal and was much lighter and more compact than the Thompson. It fired a 9mm round, which was smaller than the Thompson, and also had a slower rate of fire. It did, however, boast a greater degree of both accuracy and reliability.
The Germans were defending the beach with excellent weapons of their own. The average infantryman was equipped with the KAR 98k. This bolt-action rifle was highly accurate, although with a five-round capacity, it carried less ammunition than either the M1 Garand or Lee-Enfield. The common SMG for the German infantryman was the MP40. It had a thirty two round magazine and fired 9mm rounds. It was distinct from the Allied SMGs, however, in its accuracy. Boasting an effective range of about 100 meters, it could fire accurately at twice the range of the American Thompson. Finally, the Germans employed one of the finest light machine guns of all time in the MG42. Notorious for both its accuracy -- it could hit effectively up to 1,000 meters -- and rate of fire -- approximately 1,200 rounds per minute -- the MG42 was a terrifying weapon to behold. Firing from fixed defensive positions such as the Germans occupied at Normandy certainly added to its lethality.
Well, there are certainly many more guns and vehicles that were involved in D-Day and my overview is certainly non-exhaustive. I thought it best to give a general overview of the weapons used by the troops on the ground. Hopefully, I did that. Perhaps someone else with more knowledge than myself on the subject can fill in the gritty details on landing craft or finer points on the weaponry.