It's actually simple if you follow these rules:
1. Every device (game, DVD/Blu-Ray player, cable box, etc.) you connect to the TV needs one cable connected to the TV for video, and one cable connected to the TV for audio. HDMI is the only exception; a single HDMI cable carries both video and audio.
2. In order of best to worst quality, video connection types are: HDMI or DVI, Component (3 plugs red/blue/green), S-Video, composite video (yellow plug). Always use the best quality connection that's available on the device. Note that you can't get HD with S-Video or composite video.
3. In order of best to worst quality, audio connection types are: HDMI, optical digital, coaxial digital (the coaxial cable looks like a TV cable), analog (2 plugs red and white).
Other notes:
- Some TVs have VGA connectors which might be labeled VGA or PC. These are similar quality to HDMI or DVI, but don't include audio.
- Some TVs have audio outputs, usually analog audio or optical. These can be connected to an amplifier, speakers, or a home theatre setup - the audio being output will be the same as whatever source you are currently watching.
- DVI comes in different flavors: DVI-D (digital only), DVI-A (analog only), DVI-I (integrated, digital & analog), M1-DA (integrated, digital, analog & USB)