Wireless Connection
All PS3 controllers are wireless; the very first Sixaxis controllers communicated with the PS3 using Bluetooth, and the more recent DualShock 3 controllers do the same. This makes it easy for you to play video games without always dealing with a mess of cables or worrying about someone tripping over the controller cord. The controller runs on a battery that of course needs to be recharged sometimes, and you can connect it to the PS3 using its USB cord for this.
Charging the Controller
To charge the controller, you just need to plug its cord into the controller itself and into a free USB port on your PS3. As long as your PS3 is turned on, the controller will charge, and you'll see the LEDs blinking on the controller. When they stop blinking, the controller is fully charged. While the controller is plugged into the PS3 and recharging, it's also communicating with the console, so you can use it to play video games while it's recharging.
Controller Status and Settings
You can check on the battery charge level of the controller anytime it's on. Just press and hold the "PS" button for a couple of seconds, and you'll see the battery status on the screen. You can also set the controller to automatically turn off after a certain amount of inactivity; that way, you can conserve battery power if you stop using the PS3 for a while. This option is available in the "Settings" section of the XMB menu under "Power Save Settings," then "Controller Auto-Off."
Other Charging Methods
You can connect your controller to nearly any device with a USB port to recharge it. That means you could connect it to a PC or a laptop, though you cannot use the PS3 controller to play computer games. Sony also offers the DualShock 3 Charging Station, where you can dock either one or two controllers when you're not using them, and they'll begin recharging right away.