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.
White is doomed. Black's material advantage is overwhelming. Black wins by trading the pieces away. White's chances go away too. It will come down to Black's Q overpowering the White R, or the Black pawns running downfield to score a touchdown. If it's Black's move:
[title "Black to move"]
[fen "2k5/1pp2p2/p5p1/3b4/2NBq2P/1PK1N1r1/P7/3R4 b - - 0 1"]
1... Bxc4 2. bxc4 Rxe3 3. Bxe3 Qxe3+ 4. Rd3 Qe1+ (4... Qxd3 5. Kxd3 Kd7)
White has no immediate threats and can't really lose more material. So the exchanges are rather forced. The reason I recommend trading the pieces off here is that Black has a significant material advantage. Each even trade makes Black's remaining pieces relatively stronger. In addition, Black can create passed pawns on both sides of the board. Black can trade his Queen for the Rook and have an easy win that way, if he wishes.
If it is White's move, it isn't so easy because White has no moves. I can't really think of a good move. 1. Rd3 maybe. The only thing White has is a cheap-shot checkmate by Bf6 followed by Rd8#. It is unlikely Black will let him do it.
Regarding your other question, how could you figure this out, there's really no way except to try. You're on the right track when you count points and know Black is way up. After that, you examine the board and come up with a strategy. My strategy for this position is to trade pieces. So then I ask myself, "how can I do this?". The Bishop capture on c4 was the first thing I saw. I realized he had to recapture, so he had 2 choices, pawn or King. If he used the pawn, I'd weaken his pawn structure even further - disconnected pawns are weak. So that was good. It's a combination of having a strategy, then looking for tactics to implement the strategy. When I see a poorly placed King and I have my Queen, I am trying to find forks everywhere. Or pawns that can't defend themselves. The Qf2 queen move forks the a and h pawns. One will drop. I am not too worried about White's Rook because if it gets too far from his King, I'll be able to grab it.
The material imabalance is BAD, like so bad that the only hope is a fortress. And a fortress is impossible due to some 1...g5 stuff followed by 2...Rxe3 3. Bxe3 Qxe3+ among onther things.
This is winning for black after 1. ...Bc4 2.bc Re3 3.Be3 Qe3. Even if white could somehow avoid losing a pawn or two in this line, black can create a passed pawn on the kingside and then use the queen to usher it up to the 8th and increase the overwhelming material advantage.
