Take the peeled, cooked and cooled potatoes and cut them into sections. Using one section at a time, press them through a potato ricer. Alternatively, mash them well so that no lumps remain.
In a large bowl add the riced or mashed potato, salt, olive oil, and flour and using clean hands mix the ingredients together and then squeeze to gently knead it into a cohesive ball. If the mixture is sticky add flour until it no longer sticks to your hand. If you can't get the flour to fully absorb and mix into the potatoes add a little extra olive oil until it comes together. The key is to not have a wet and sticky dough so that it's easy to work with and form into little dumplings.
Keeping the dough covered so it doesn't dry out, take a small section at a time to form into the gnocchi. Take a 1 tsp (~6g) piece of dough and squeeze it in your fist to make a compact and roughly shaped ball, then roll it between your palms to make it round.
For the traditional gnocchi shape with the grooves on one side, place a fork sitting face down on the counter and take the ball and place it at the top of the backside of the tines of the fork. With your thumb on the piece of dough, slide the gnocchi down the tines of the fork until you reach the counter. The gnocchi will turn under your thumb until it has grooves going around about ¾ of the dough and a small inset divot where your thumb was.
Repeat with remaining pieces of dough. If the dough becomes sticky at any point, toss shaped gnocchi with flour so they don't stick together and knead a bit of extra flour into the remaining unshaped dough.
To cook the gnocchi, bring a large pot of salted water to a boil. Add half the gnocchi to the pot and let it cook for about 4-5 minutes, or until the gnocchi float to the top and have cooked an additional minute at the top. Remove the cooked gnocchi with a slotted spoon and then cook the second batch of gnocchi.
Use the cooked gnocchi in your favorite recipe, or store in the fridge for up to a week (you can freeze for longer).