How do I hook up a powered subwoofer to my HDTV?

You can't ... at least not directly. You need to introduce an amplifier between the TV outputs and the subwoofer. If you do go this way you should also add (at least) two speakers. Most HDTVs don't have red/white stereo audio OUTPUTS (you may be confusing INPUTS) and only have an optical output. IF yours does have stereo outputs you can either use a small dedicated amp like that at the 1st link, or use an AV receiver. The wires from the speaker terminals on the mini amp (or connect the RCA subwoofer output on the AV receiver to the RCA input on the sub) go to the input terminals on the sub, and the new speakers (if you add them attach to speaker output terminals on the sub. If you use the mini-amp you set the crossover on the sub. If the output on the TV is actually an optical you need to use an AV receiver connected with an optical cable. You turn off the crossover on the sub (or turn it to the highest frequency) and let the AVR handle the crossover (See 2nd link). You will also want to turn off the internal TV speakers and enable the external speaker jacks.

From reading the description of your subwoofer and the way you intend on hooking it up, I believe you have misunderstood the capabilities of your subwoofer. For one, the single input is usually hooked up to the LFE output of a surround sound reciever and not connected directly to a tv. Also the connections you believe to be for other speakers may actually be speaker level input/output (do you have speaker input connections as well as speaker output connections?) After all, how would you get the left and right stereo sound if your subwoofer only has one input? Another possibility is that the sony subwoofer that you are trying to use was meant to be used with specific sony equipment and that the capabilities you are trying to get from it cannot be acheived with anything else.

You can not connect any speakers to a tv, they do not have enough power to drive any speaker except what it came with. You have to connect the tv to a receiver first then connect the subwoofer to the receiver. When you connect the subwoofer the optimal setting would be at 80HZ, if you have speakers connected to the subwoofer the it will depend on the speaker what it is capable of covering in the low range. Hope this will help you out.