user13147: 1rr3k1/p3p1b1/b2p2pB/q2P1p2/4P3/1PNn1PK1/P1RQN1PP/7R b - - 0 23

In the above position (reached after 1. Bxh6?) Stockfish points out that Black has a winning move, going from 0.00 to -2.25.
However, I cannot find the tactic. Here are some details I have pointed out.
Checks: Black can check with Be5+ or f4+.
Captures: Black can capture the knight on c3 if a defender is removed: There are three attackers and three defenders on the square. The Black knight on d3 is protected by the bishop and is not hanging, so it cannot be captured. White can capture the g7 bishop, an attacker of c3, on the next move.
Threats: White cannot take the pawn with the knight after 1... f4+ because that removes a defender of c3. White cannot take with the king either because that interferes with the queen's defense of h6, and thus Bxh6 is possible (skewer). The intermezzo 2. Nxf4 does not work because of 2... Bxc3, attacking the queen.
Please only provide hints and not the actual winning move. What are the tactics (such as deflection, coercion, attraction, etc.) that Black should look for?

user12629: I see you looking at "forcing" moves such as checks and captures.  This is probably a good place to start.  One of the best features about "forcing" moves (especially checks) is that the opponent is limited in their possible responses. Both checks you have available, for example, allow only six possible responses; that's way easier to calculate than the 36 or so moves he'd otherwise have.  A capture allows for more possible responses than a check, but most of them are obviously bad if they don't regain the material, so that also limits the required calculations.  
So, for each candidate move, go through each of their responses, one by one, and see if you have a good reply to it.  You've started this with a couple of moves; finish it for those moves, and if they don't appear to be correct, move on to the other forcing moves.  If you still cannot find it, look for other candidate moves (such as ones that create threats.) 
(I'm not going to provide an actual hint because I see someone else already did, and you probably don't want two.)

user11629: You are almost there with your analysis. Tactical motives you should look out for are:
overloading, interference, distraction, skewer

user-1: I first noticed that the knight on e2 seems to be overloaded, defending both the knight on c3 and the f4 square.
f4 looks interesting, because there are 2 ways your bishop can control that square, potentially pinning a piece that lands on it to either white's king or queen.
I don't want to analyze more than that, you asked about how we would approach finding tactics. Look for overloaded pieces, pinning squares, discovered checks, etc.

13147: <pre><code>1rr3k1/p3p1b1/b2p2pB/q2P1p2/4P3/1PNn1PK1/P1RQN1PP/7R b - - 0 23
</code></pre>

<p>In the above position (reached after 1. Bxh6?) Stockfish points out that Black has a winning move, going from 0.00 to -2.25.</p>

<p>However, I cannot find the tactic. Here are some details I have pointed out.</p>

<p>Checks: Black can check with Be5+ or f4+.</p>

<p>Captures: Black can capture the knight on c3 if a defender is removed: There are three attackers and three defenders on the square. The Black knight on d3 is protected by the bishop and is not hanging, so it cannot be captured. White can capture the g7 bishop, an attacker of c3, on the next move.</p>

<p>Threats: White cannot take the pawn with the knight after 1... f4+ because that removes a defender of c3. White cannot take with the king either because that interferes with the queen's defense of h6, and thus Bxh6 is possible (skewer). The intermezzo 2. Nxf4 does not work because of 2... Bxc3, attacking the queen.</p>

<p><strong>Please only provide hints and not the actual winning move.</strong> What are the tactics (such as deflection, coercion, attraction, etc.) that Black should look for?</p>
 12629: <p>I see you looking at "forcing" moves such as checks and captures.  This is probably a good place to start.  One of the best features about "forcing" moves (especially checks) is that the opponent is limited in their possible responses. Both checks you have available, for example, allow only six possible responses; that's way easier to calculate than the 36 or so moves he'd otherwise have.  A capture allows for more <em>possible</em> responses than a check, but most of them are obviously bad if they don't regain the material, so that also limits the required calculations.  </p>

<p>So, for each candidate move, go through each of their responses, one by one, and see if you have a good reply to it.  You've started this with a couple of moves; finish it for those moves, and if they don't appear to be correct, move on to the other forcing moves.  If you still cannot find it, look for other candidate moves (such as ones that create threats.) </p>

<p>(I'm not going to provide an actual hint because I see someone else already did, and you probably don't want two.)</p>
 11629: <p>You are almost there with your analysis. Tactical motives you should look out for are:</p>

<p>overloading, interference, distraction, skewer</p>
 -1: <p>I first noticed that the knight on e2 seems to be overloaded, defending both the knight on c3 and the f4 square.</p>

<p>f4 looks interesting, because there are 2 ways your bishop can control that square, potentially pinning a piece that lands on it to either white's king or queen.</p>

<p>I don't want to analyze more than that, you asked about how we would approach finding tactics. Look for overloaded pieces, pinning squares, discovered checks, etc.</p>
