What source(s) are you using? Cable/Satellite, DVD, Blu-Ray, game systems?
A common misconception is that the digital audio out on TVs can be used to feed a surround sound system. This is not true in nearly every case.
Any audio that is fed into your tv from an external source (like the ones listed above) will be downcoverted to simple stereo before it is sent out of the "digital audio out" jack on the back of the TV. Only audio picked up from the TV's own internal tuner can be output in 5.1.
If you have multiple sources capable of 5.1 or better sound, your best bet is to get an Audio/Video Reciever and a set of 5.1 speakers. An A/V receiver serves as the "hub" of the system. All sources (both video and audio) are routed through the receiver. A single video cable is run from the receiver to the TV and the sound is channeled to the 5.1 speaker system. Typically, the TV's speakers (which are nothing to write home about anyway) are completely bypassed.
The most inexpensive solutions (you didn't mention a specific budget - do you have a figure in mind?) like Ed mentioned are all-in-one home theater in a box systems. Such systems are very easy to set up and convenient, but are often limited in the number of inputs available to them, and the speaker build quality is often their weakest link.
There are a number of good HTiB systems from Onkyo, Panasonic, Samsung, etc. If you can tell us what devices you want to hook up to the system, whether it's HD or not, and what sort of budget you have in mind, we can probably make some good recommendations for you.