What I do is boil the eggs, when they are done to my satisfaction, I submerge them in ice cold water; when the water warms, I drain and readd ice cold water. After about 10 min I peel and they usually come off much easier. If you are pulling off egg with the shell, they are likely too warm to be peeling.
I've also read that if you put a little baking soda in the boiling water with the eggs, they will peel easier, but I have not tried this method.
I put vinegar in my water about a half cup when eggs are cool peel from the top there is a little air pocket and if you look close there is a membrane that is very thin between the egg and the shell so try and peel under that and it should come off better the night before you want to boil them turn them upside down and the yolk will be in the middle good luck