Classic method is place the sausage in a single layer in a frying pan, add about a 1/4 to 1/2 inch of water (depending on thickness of links), and bring to a boil. Keep boiling until the water boils off (the sausage should be cooked through at this point). Once the water has boiled off, the sausage should start to fry. Depending on how much fat has rendered out during boiling, you may need to add extra oil (coconut or olive or butter or lard). Flip the sausages a couple times during frying to get even browning and crispiness on all sides.
Spanish chorizo and Portuguese chouriço can be cooked as above, Mexican chorizo is more often removed from the casing (or bought in bulk without a casing) and just fried straight in the frying pan, flipping and breaking up clumps the same way you would cook ground beef.
Two items I missed: 1) cook sausages whole, and 2) do not prick or poke the casing before they're done -- you want to keep as much of the liquid rendered fat inside the sausage to keep it moist and tender.