I'm black, and it's my move.

I'm a newbie to chess, and as such, I don't get to endgame having the lead very often. Nor do I have much experience with check mating.

Just wanted some opinions on what I should be doing here, hopefully it's not too terribly obvious

link fails

this is not from an ongoing game right?

No I just suck at posting diagrams. One sec..........

Like you said, big material advantage here, and black several ways to win. Really, white's only threat in the position is to capture on g7 and try for a perpetual by checking the white king, which doesn't work. Technically you can ignore the threat and play for mate, but I think that complicates things unnecessarily. For practicality's sake, I would play ...Qh6 when white has zero counterplay at all. If he tries to capture on g7, we simply take with our queen and we're up two rooks, so he can't try that. I'd follow up with playing ...Raa1 threatening mate, and when the g3 rook moves, you can always play Rh1+ and then Qf4 will end the game.

Cliff's notes: just guard g7 and the game is over.

Yeah this is just crushing. You should really read up on some beginner material if this is hard to you, for instance Silman's columns on chess.com

You basically have to protect the g7 square with your queen and then exchange your rooks for his rooks. If he moves his rooks to avoid the exchanges then attack his pawns.