How do you boil eggs without cracking the shell?

Use room temperature eggs. If kept in fridge (as they do in N America) then put in a pot of warm - not hot - water to bring up to room temp...then proceed. Vinegar will help keep whites tight when water poaching, but does nothing for preventing cracking the shells when cooking.

Prick the end that holds the air with a pin.

I've heard adding a capful of white vinegar to the water can keep them from cracking.

How boiled do you want them? I like mine with the whites set and the yolks still runny. So i use the same technique that burn toast does. For large eggs about 3 min, x-large 3 1/2. Jumbo 4. However, it depends on the amount of water in pan. Huge amount takes longer to come to boil, so less time after boiling.
Not very precise, sorry.
Best of all in a circulator at 143F for 45 minutes. But that is a bit over the top!

Add your eggs to cold water. Bring to boil then immediately turn off heat. Set timer for 13 minutes. Drain eggs and run under cold water until cool. Peel under cold running water or refrigerate for later use.