For meat, your best bet is a meat thermometer. Try to get one that’s labeled with the different kinds of meat so you don’t have to remember the exact number of degrees that make them safe to eat. Otherwise, you’ll have to make a cut down into the center of the meat and see if it’s still pink and raw-looking, and/or letting out blood instead of clear juices. Of course, once you’ve made the cut, the meat inside it is more exposed to the heat, so if you need to check again later, you’ll have to make a new cut. It can get messy.
To make sure the meat is ready on time, there are several things you can do. For a roast, give it more time than you think it really needs. If it sits for up to 20 minutes before being eaten, not only will it stay hot, the juices get a chance to redistribute evenly. For smaller, pan-cooked pieces like sausages, you can cook first, then brown, by putting both fat and a little water — enough to cover the bottom — in the pan. When the water boils off, see if the meat is cooked through, and if not, add a little more water. When the meat is finally done, let the fat take over and brown the outside. In emergencies, when the outside of a piece of meat is done or overdone, and the inside is still undercooked, you can steam it with a few minutes in the microwave. This will change the taste and texture somewhat, but it’ll get the meat cooked to a safe temperature without burning the outside.
Baking, of course, is done when you can stick a toothpick or knife into the center and pull it out without any batter clinging to it (except for yeast bread, which is done when it sounds hollow when hit). The best way to make sure this happens just as the outside is lightly browned is to use the right size pan. But if that doesn’t work out for you, there’s always the microwave option — after moving the food to a microwave-safe dish.
Unlike undercooked meat and egg-bearing batter, undercooked potatoes won’t actually make you sick, but they’re no fun to try to eat. Potatoes are done when you can stick a fork into them easily. If you’re using them for mashed potatoes or something similar, cut them up fairly small to make this go faster. If you’re baking whole potatoes, give them at least an hour in the oven at 400 (be sure to make a few knife cuts in them to let steam escape so they don’t burst). Yes, they’re something else you can finish off in the microwave, but if you know you’re short on time, you might think about starting them in the microwave for a few minutes instead. Then the skins can still come out crisp.
Take the time to cook things through.