Once you have a short list of cars in your price range that meet your required criteria, it's time for some test drives. Before you begin, promise yourself that you won't buy any car until you've finished test-driving all the candidates. Call several dealers in your area, and describe the car you want, and ask if they have one there that you could test drive. Only schedule an appointment if they confirm that they have a car that meets all your requirements.
Take a copy of your car key and a photocopy of your driver's license with you to the dealership. They will usually ask you for your car keys and your driver's license before the test drive, which is reasonable, but some unscrupulous dealers will "misplace" one or both to give them more time to sell to you. If you have a spare copy of the key and a photocopy of your driver's license, that protects you from this trick.
You may also want to bring along one or more people on the test drive, such as a friend who happens to be a car expert, or anyone who will be driving or using the vehicle frequently.
For each car you test drive, record the Vehicle Identification Number (VIN), which usually appears on the driver's side near the bottom of the front windshield. Get a copy of the sticker (including the mileage if it's used), or write down the information if the dealer can't provide you with a copy.
During the test drive, don't be timid. You want to test as many different driving conditions as possible, and you only have a few minutes. Try fast acceleration and braking, sharp turns, bumps, and anything else you can think of. Be especially thorough if you're buying a used car rather than a new one. See if the car feels comfortable. See if it has a blind spot. See if you can parallel park it easily. Turn off the radio and roll the windows down, and listen for any noises. Ask the dealer a lot of questions. Some dealers will allow you to take the car for an extended test drive on your own; do so whenever possible, as it will enable you to get a much more thorough feel for the car.
Once the test drive is done, move on to the next dealer and repeat the process. You will not be buying a car today, so there's no point in starting to negotiate with them. If they give you a price, ignore it. Many dealers will give you a price that seems unbeatable, so that you'll come back to them to buy the car. The problem is that when you come back, you won't get that price. So don't even start playing that game.