It depends how you like your roast potatoes! Personally, I hate the texture of roast potatoes with semolina coating or the waxy potato type some chefs make as they keep their shape better.
I use floury potatoes (so they are fluffy inside) like King Edward or Maris Piper potatoes. They are the classic varieties to use for roast potatoes.
Peel and chop to even sized pieces. You can either par boil for 10 mins so the outside is soften then rough them up by shaking the pan or with a fork, or (which I prefer) use the Heston Blumenthal method of boiling until almost falling apart.
Duck or goose fat or beef dripping are the best fats to use, about 2 tablespoons should be enough but you want enough to baste your potatoes and the entire base of the pan to have a thin coating. Melt it in the oven at 190C or 180C fan, then add the potatoes and baste.
I generally turn them and baste after 10 minutes, then again after another ten minutes, then regularly check them and turn and baste as necessary so each potato is cooked evenly. It usually takes about an hour but that depends on how many potatoes there are are and how spaced apart they are.
You can start them off at a higher temperature for ten minutes (about 220C) to cook them more quickly but I find cooking them for longer at the same time as the roast works just as well and is more convenient. If they are cooking too quickly, you can take them out when they are almost done and then put them back in for 10 minutes to crisp them at the end of cooking everything else. If they aren't ready at the end of cooking, ten minutes at 220C will finish them off while the meat rests.