Where Do I Connect This Power Cord?

That looks like a 4-pin fan plug. Assuming that it is, either find a 4-pin fan header on the mobo and plug it in, or grab the card manual (or take the card out) and find the 4-pin fan header on the card.

The latter is preferable, because your card (what model) is more likely than not to have a speed controller that slows down the fan when the card is cool and happy.