This problem depends on how many red lights there are. The problems can be from a corrupt hard drive, to an overheated console. In this solution, I will mention all problems, and solutions.
1 Red Ring means hardware failure in your Xbox console. It can also mean hard drive corruption. There are multiple solutions to this problem. Turn off your console and unplug every single cord, cable, and memory device on your console. Wait about twenty seconds, and plug everything back in into it's origanal spot, and make sure everything is connected correctly. If the problem still occurs, try unplugging the console's hard drive, then turn on your Xbox 360. If your console then works after this, it could mean your hard drive is corrupt, or broken. Make sure to also disconnect all other memory units out of your console, such as a memory card. If the problem continues, contact Microsoft Support at the following link.
2 Red Rings means that your Xbox 360 console is overheating. Overheating is a common problem with Xbox 360 consoles. Turn off your Xbox console. Make sure it is in a roomy spot, and not near a heated spot. Also make sure it is not on top of a towel, or anyplace cluttered. As seen here,
NEVER cool off a Xbox 360 in a refridgerator, or freezer. This may cause further problems to your console.
3 Red Rings means there is a hardware problem, or something wrong with your power supply. To solve this, make sure the color on your power supply is always orange, when your Xbox 360 is off. Also make sure the color is always GREEN when it is on. If it is RED when you turn your Xbox on, try unplugging every cord, cable, and memory device on your console, and plugging it back in about 20 seconds after, and make sure all plugs are connected securely into it's socket. If this does not resolve your issue, contact Microsoft support at the link at the following link,
4 Red Rings indicates that there is no audio/video plugs detected from your AV plug. This is a simple problem to fix. Make sure all plugs are connected firmly into the correct color sockets on your TV. The following colors are the ones that need to be plugged in a Flat Screen TV,
2 Red, 1 Green, 1 Blue, 1 White. As seen here,
Although, on a small, old TV, you usually only need to connect the yellow, and white cables. Make sure if you're using an old TV that does not support HD, switch the AV cable to 'TV', if it is switched to 'HD'. If this does not work, you may have to buy a new AV cable.
I hope this helped you, and the Fixya community! Contact me if you're still having trouble!