Basic Computer Troubleshooting

Sometimes it seems like your computer has a mind of its own. You wake up one morning, and the machine decides not to boot. Another day, you can't print. Or your Internet connection starts to act up. Modern computing is filled with such apparently random problems, and when they occur, it's often hard to figure out where to begin. Is the problem hardware-related or software-related? Can you fix it without shelling out some cash?