Welcome to the forum.

The 15-pin sub-D cable is your standard computer monitor cable, also known as a VGA cable.

That's probably the easiest way to hook your television up to your computer. On the back, there is also an audio in 3.5mm to 3.5mm (from laptop output to televison input) next to the VGA input on the television.

Most laptops have a Function Key combination to send the video signal out to the external monitor (in your case, television). Once you have the VGA hooked up to both the television and the computer, and both are turned on, press the FN+F8 combination (Dell's output signal toggle), and your picture should appear on the screen if it's set at a supported resolution.

Keep me posted.