The most straightforward way seems to be using a VGA to HDMI adapter, then connecting that to an HDMI capture card. I have an Elgato Game Capture HD for other capture duties that I'd like to keep ...

But if you want to connect a computer to your TV (or you've got a new computer monitor), the options tend to be HDMI, DisplayPort, DVI, and sometimes old-school VGA. Each connection has its pros ...