I use boiled eggs mostly for recipes where you want the yolk solid all the way through (but not one bit overcooked). If the yolk is at all darker on the outside than it is on the inside it's overcooked. If the yolk is green on the outside you need to sign up for remedial water boiling.

Hopefully you're eggs have been stored pointy end down. If not, give 'em a spin on the table top to realign the innards. Preferably you have an egg piercer - snap the round end to punch just a tiny hole through the shell which will minimize bursting eggs. Put them in a pot and add cold water to cover.

I toss a bit of salt and vinegar into the water which are supposed to make the eggs peel better but I haven't tested this and I suspect it doesn't have much effect. Some chickens lay peelable eggs and some lay eggs that'll look worse than the moon by time you get the shell off, if you can get it off.

Cover the pot and put it on high heat. When it comes to a full boil (you'll hear the eggs rattling in the pot) turn off the heat and leave covered. When the water's cool enough to stick a finger into it the eggs are done to perfection. Chill in cold water and peel.