Although specialist cables allow you to connect an iPad to most TVs, if you want to make a wireless connection you must use a system called AirPlay. As of May 2014, no televisions directly support AirPlay. Instead you must buy a set-top box called Apple TV. As of May 2014, this costs £99 in the UK.
Connect the Apple TV device to your television using either an HDMI cable or component video cables. If you use component video you'll need to make a separate audio connection using analog or optical digital cable. You can instead connect the audio to a surround sound speaker.
Plug in the Apple TV to the mains power then follow the on-screen instructions using the remote control to set up the device. You'll need to select your wireless network (or input the details manually) and input the password. When you are done, your TV will display a five-digit code.
Make sure your Apple TV and iPad are both connected to the same wireless network. Open the Music, Photo, Safari or Videos app on your iPad and tap the AirPlay icon, which is an upwards triangle pointing into a rectangle (representing a TV). If you want to watch a video in Safari or the Videos app, you'll need to start playing it on the iPad first to be able to access the AirPlay icon. Once you press the icon your iPad will display a list of devices: select "Apple TV" to play or display the content on your TV.
You can also mirror your iPad on the TV, meaning whatever is on your iPad screen is also shown on the TV, allowing you to run any application. To do this, double-click the home button on the iPad to reveal the recently used apps list. When you swipe through this, you should see an AirPlay icon (even if it's the first time you've used the feature). Tap this icon, then tap "Apple TV" from the device list and slide the "Mirroring" toggle to "ON". You can also play content from your iTunes library through the Apple TV device. To do so open iTunes on your PC or Mac. Look in the devices list for the Apple TV icon and click this icon. When prompted, type in the five-digit code. This "pairs" your computer and Apple TV device. You can buy Apple TVs online or get one from an Apple retail store.