Why does my homemade pasta stick to itself whilst cooking?
I have that problem when I am impatient and don't let the pasta dry out long enough before putting it on to boil.

It is important to let the pasta dry even just in loose little heaps once sliced into noodles.  It doesn't have to get totally dry just dry enough that you can't squish the noodles back together into dough.

Also you need to cook fresh pasta for a very short amount of time in a LOT of water, about 1.5x as much water as you would use for dry, so that the noodles have less chance to run into each other.  In fact I frequently don't boil them at all separately but just toss them in the soup I am serving them with for for a two to three minutes before serving.