Always start with room-temperature eggs, if your eggs are cold they can crack in the hot water.
Some recipes will say to place eggs in cold water, I don't like this method for various reasons, one is I find that you can overcook your eggs too easily so I suggest you stick with the hot water method.
I would also suggest that you set a timer, a minute or two can take your egg from soft to hard, also remember if you drop your eggs in cold water, you stop the cooking process and this will make peeling easier.
Make sure that after your water reaches boiling point, you turn down the heat so when you place the eggs in the water, the eggs don't bounce around and crack. After the eggs are in the water you can turn the heat up again. Don't place too many eggs in the pot, leave some space around each egg to cook.
You can store your boiled eggs in the fridge - soft-boiled eggs for up to 3 days and hard-boiled ones for 1 week.
How to test the freshness of your eggs:
Perfectly Boiled Eggs: