How to cook sausage?

Sausages are pretty forgiving. As long as you don't burn them or leave the center raw, they should come out OK. Since they're pretty fatty (at least the good ones are) there's little chance of drying them out, so when in doubt, cook them a little longer. They'll feel firm, not squishy, when they're done.

The easiest way to cook raw sausages is in the oven (at 350-375°F, 180-190°C or so). If you're doing it on the stove, I'd brown them first in a little (very little) oil, then add some water, or beer, or wine, or whatever you happen to have (not much - just enough to cover the bottom), cover, reduce the heat, and simmer until done. Feel free to cook some vegetables in the pan along with the sausage.

Use your oven and bake at 150°C (300°F) for about 50 to 60 minutes. They should be crisp skinned, fully cooked (for taste and food safety), but still soft to the bite

If you run the oven any hotter they may split or explode

Section the sausages and lay them out evenly on an oven tray (with some edge or 'lip'). You can pack in as many as you can fit into one layer. No oil needed. Place in the middle of the oven and relax

For very fatty sausages you may wish to drain the fat off one or two times during cooking

Using a frying pan is fine but it usually causes uneven cooking and burnt spots

To be super safe, boil them covered in water for 15 mins, then sear in a lightly oiled very hot pan.

Are they loose or in a casing?

If they are loose then you should be able to cook them just like you would ground beef. Sausage is generally fairly fatty so you shouldn't need to add any oil or anything. I'm more familiar with chorizo which tends to be quite fatty, but if the others seem a bit dry you could always add a touch of oil to help them along.

If they are in casings then you could either remove them from their casing and cook them as above, or just cook them directly in their casing. A little bit of oil or butter in this instance might help, depending on how well they are sealed up, but again this is probably unnecessary for most sausage.

I like to cook mine on the grill for 40 minutes or so, 20 minutes per side. Crisp and tasty!

i'm in the long and slow camp when time allows. i like to fry them in a little butter over a low heat which can result in a nice sticky outside. often i'll throw some sliced onions in there to soften in the sausage fat. Mmmm...

like the others have said the thing to watch out for is to make sure they are cooked through. And please, don't prick them. that just lets the fat out and risks drying out your sausage.

For the types of "real" sausage you mention I'd be tempted to make a risotto and add diced sausage after about 5 minutes.

The flavour would soak out into the rice quite well, and for Chorizo - so would the colour.

These kind of sausages are cured so I'm not personally that bothered about cooking for an extra long time as they are already edible, although you might not be that happy with the taste.