It's tempting to start pasta in cold water if you're in a hurry and don't want to wait for the water to boil, but try to resist the temptation if you're working with fresh pasta. Starting fresh pasta in cold water can cause the pasta to absorb too much water and become mushy.
On the other hand, dried store-bought pasta can be started in a pot of cold salted water and brought to boiling without ruining the pasta's texture.