Herein lies the biggest challenge for a new cook, I believe: knowing when something is done. Unfortunately, the most common way to check for doneness of, say, a piece of meat--cutting it open--is also the worst way. Cutting meat while it's still cooking is a good way to get really dry meat. Along with ways to check for doneness of meat, I'll also go through a few ways to ensure that you do not have doughy breads or gooey quickbreads. So, here we go.
The Thermometer Method
Used for: Meat, primarily
Certainly, this is the most accurate way to check for doneness. I would suggest purchasing a digital probe thermometer which has a cord connecting the probe to the readout. This way, you can check on an item in the oven without having to open the oven. You can also set an alarm on the readout which will tell you when it's done.
A couple of rules about this method: First, make sure the end of the probe is as close to the center of the thickest part of the item as possible. Also, make sure it is not touching a bone as this will cause a false reading. Once the item has reached the desired temperature, leave the probe in there for a few minutes (3 minutes for small items up to 15 for things such as a roast or turkey).
You should cook the following items to the following temperatures (all Fahrenheit):
Poultry of any kind - safe to eat at 165°, white meat is most pleasant to eat at 161°, dark meat at 175°
Ground meat of anything but poultry - 155° is safest
Other solid meats - 145° is safest
Doneness levels of things like steak - 125 °=rare, 130 °=med-rare, 135 °=med, etc.
Yeast breads - 190°
The Poke Method
Used for: muffins, cupcakes, quickbreads
When you poke the top of one of these items, it should spring right back. If your finger leaves a dent, let it cook longer.
The Other Poke Method
Used for: meat, esp. steak
Hold your hand relaxed and open, and then press your finger against the fleshy part near your thumb, that's what a rare steak should feel like. Now touch your thumb to your forefinger. This is what a medium-rare steak should feel like. Each successive finger represents the next level of doneness.
The Toothpick Method
Used for: cakes, brownies
Stick a toothpick in the middle of the item. It should come out clean.
The Jiggle Method
Used for: cheesecake, quiches, frittatas
If you shake the pan, the contents should still have some jiggle when you take it out of the oven or off the stove. If you only see jiggle within the center third or less of the item, you're good.
The Bubble Method
Used for: pancakes
When you see bubbles really start to get going on the top of a pancake, flip it. Then, cook the other side to a nice golden brown. (It's okay to peek.)
The Tasting Method
Used for: pasta, veggies
Sometimes, the best way to check for doneness is just to eat some of it. It should go without saying, but don't do this with anything that isn't safe to eat raw.