[/url]Adding an Apple TV would be the obvious choice. AirPlay works well. Once the tablet and the Airplay device are on the same wireless network then simply swiping up on the tablet screen opens the AirPlay window. It's then just a matter of selection where to show the tablet display.
But if your TV hasn't got a HDMI socket then you're really going to struggle I think.
If you are happy to invest in some additional hardware then you can use AirPlayer as an application as part of an XBMC install. You'll still need a host PC though and, at the least, a VGA input on the TV.
[url]http://lifehacker.com/5802958/how-to-make-your-entire-home-airplay+compatible
That's really good info. You can use a Raspberry Pi to run XBMC...
http://cpc.farnell.com/1/1/114355-raspberry-pi-xbmc-starter-kit-rpi-xbmc-starterkit-pro-signal.html