Preheat oven 425F.
In a medium pot, bring the water and butter to a simmer on medium heat. Add the flour and with a wooden spoon or spatula, stir very quickly in one direction. Carefully watch and you'll see that the flour starts absorbing the liquid -- and a dough will form. Keep stirring to continue cooking the flour and cook off some of the water, another minute or two.
You can do the next step one of two ways:
Transfer the paste to the bowl of a standing mixer fitted with the paddle attachment or to a bowl if you're using a hand mixer.
If you want to mix the eggs directly into the dough in the pot, let it cool slightly, 4 or 5 minutes, or cool off the pan itself by running cold water over its base if you will be mixing the eggs in that pot. You don’t want to cook the eggs too quickly.
Add the salt and the eggs one at a time mixing rapidly until each is combined into the paste. The paste will go from shiny to slippery to sticky as the egg is incorporated. The pâte a choux can be cooked immediately at this point or refrigerated for up to a day until ready to use.
Spoon the dough into a large gallon-sized plastic bag (or piping bag.) Use your hands to squeeze dough towards the bottom corner. With kitchen shears, snip off just the tippy tip of the bag, about 1/4" of the tip. Pipe onto a baking sheet into little puffs, keeping the puffs 2-inches apart. With your finger, press down the peaks (as they can burn.) Bake at 425F for 10 minutes, then 350F for 18-30 minutes, depending on the size of your puffs.