Once the potatoes are cooked, wait until they’re cool enough to handle before you peel them. While some cooks make gnocchi with hot potatoes, in my non-scientific tests, I found the negatives (handling hot potatoes and the possibility of the eggs cooking when they hit the hot potatoes) outweighed any benefits.
To prep the potatoes for the dough, pass them through a potato ricer or food mill. If you don’t have a potato ricer handy, you can grate the potatoes or mash them. (In fact, you can make small batches of gnocchi with cold, leftover mashed potatoes!)