I would like to connect my computer to my HDMI-enabled monitor. The computer has a VGA out and one of these:
I don't know what that is called.
That's a DisplayPort socket. Display port to HDMI adaptors are available, almost always DisplayPort is set up as displayport dual-mode, meaning a simple, cheap cable adaptor—e.g. this randomly selected two dollar jobbie from ebay —will suffice for connecting it to HDMI equipment.