Who has the advantage at this point in the game? I was playing the following game and at this point I thought black had the advantage but upon thinking about it for a little while was not sure.

At this point in the game who has the advantage and by "how much"? …and I don't mean just counting piece points which I know how to do—I mean taking the positioning into account as well.

Additionally, how could I figure this out myself without bothering the folks on Stack Exchange?

[fen "2k5/1pp2p2/p5p1/3b4/2NBq2P/1PK1N1r1/P7/3R4 b - - 0 1"]
In this position, the material imbalance pretty much tells the whole story, as a queen and two pawns against two knights is, barring significant positional compensation, an overwhelming material advantage. And in this case, the non-material positional considerations only serve to emphasize Black's advantage: the white king is exposed, and his pieces are not well coordinated (one knight pinned, and the remaining forces at risk of becoming overloaded trying to protect one another). The upshot is that White is powerless to prevent Black from further increasing her (already winning) material advantage, liquidating to a situation in which White has nothing left to play for or with. Resignation wouldn't be unreasonable for White.

To illustrate, if Black has the move (the OP doesn't say whose move it is), then 1...Bxc4 already yields 2.bxc4 Rxe3+ 3.Bxe3 Qxe3+, when Black has a queen and two pawns for a rook, and can win at her leisure. But even if White has the move, he is so tied up in knots that he can't stop that operation (or something similar). For example:

[FEN "2k5/1pp2p2/p5p1/3b4/2NBq2P/1PK1N1r1/P7/3R4 w - - 0 1"]

1.Re1 
    ( 1.Rd3 Bxc4 2.bxc4 f5 3.Kd2 f4 )
1...Bxc4 2.bxc4 f5 *


Black can continue to pick up material with her queen in the open field, and White won't even have an army with which to dream of mounting an improbably comeback.