You're going to need to connect a cable supported by BOTH the PC and HDTV. Check your HDTV's jack panel or manual. List the types of Input jacks it offers. The HDTV will likely have Component, Composite, DVI, HDMI and maybe even VGA jacks. Do the same for your PC. It likely has one or two Video Output jacks. Typical Video Outputs are DVI and VGA. The VGA type has been standard for years. It consists of a total 15 pins in 3 rows. The DVI has a number of pins, but most noticeable is a wide tab at one end of the jack.
If your HDTV has a jack that matches one of those found on the PC, you're in luck. Purchase a cable that will connect them - this would be either a VGA cable or and DVI cable. Nearly any inexpensive VGA or DVI (Digital Video Interface) cable 6 ft or less will do, but the better cables cost a bit more and when the distance is increased, the quality (or lack thereof) really becomes visible - especially
on the lager HDTV screens.
If you want the sound to go to the TV speakers or elsewhere, you'll need to get a cable with a 3.5mm stereo plug (or whichever type your PC has - but that's the most common) to RCA or whatever the audio input jack type is that is associated with the video input you chose
. The audio input must be the one associated with the video input - other wise you will not hear the audio on input 4 while watching input 3. The PC audio out is analog, so do try to put the signal into a digital input.
If you don't have a matching video input jack, you'll have to purchase an adapter or new video card with jacks that match your TV. Do not buy simple adapters that change VGA to DVI as they will not convert the actual analog VGA signals to Digital Video signals expected by the HDTV's DVI jack. The best bet is to buy a modern video card supported by your computer's mother board and OS that has a fair amount of memory (512 MB is a good start). If your HDTV has HDMI jacks and you wish to play the sound from the HDTV's speakers, get a card with HDMI output and buy an HDMI cable. It will send both the sound and video to the HDTV for you.
You can read a nearly endless list of articles about HTPCs aka "Home Theater Personal Computers" for ideas and deep discussions about everything from soup to nuts to implement, design and set up on google
I hope this helps - good luck!