The general process is to use the ideas to identify specific candidate moves. Next, calculate each move to the end and evaluate the final positions (material and activity). As you progress through the candidates, keep in mind your "king of the hill" (KOTH) candidate move to help you pick the best at the end.
The first defensive idea is to do something to the piece creating the threat: capture, pin, or deflect it. Of course when you are in check you have no time to pin or deflect the piece, but any other kind of threat gives you more time and therefore more options.
Black just played Bd8 to block white's d-pawn and attack the queen. White to move.
Idea 1 (capture, pin, deflect): Qxd8; can't deflect or pin the bishop to anything of equal/greater value (the queen or king).
Idea 2 (block): none
Idea 3 (move): Qf5, Qe5, Qd5, Qf4, Qe3, Qd2
Idea 4 (defend): Does not make sense to defend the queen here.
Idea 5 (counterattack with an equal or greater threat to WIN, DRAW, DEFEND): an equal threat would be to attack black's queen; a greater threat would be to attack black's king. Rd6 attacks the queen; h6 might be interesting since it threatens a capture-check.
That gives us nine candidate moves to calculate. Let's start with white's most forcing move first, and look for black's possible refutations: 1. Qxd8:
White is now up a bishop and a pawn, and is threatening to win black's rook with 2. Qxg8+ Kxg8 (only) 3. d8=Q+.
1...Rxd8 2. Bxd8. Material is now equal (R/B/PvsQ), however, white's threat is to promote his pawn to a queen in two moves, leaving white up an entire R/B. Black has no way of stopping the pawn from promoting without giving up his own queen. Black should reject 1...Rxd8.
A quick search for other candidate moves for black yields nothing: 1...Qh6+ allows the simple block 2. Qg5. 1...Qa8 (defending the rook) allows the simple 2. Qxa8 (any) 3. d8=Q. 1...Qe6 (again defending the rook) still allows 2. Qxf8+ (any) 3. d8=Q.
This makes 1. Qxd8 our KOTH. Now, in an actual game with time controls white can stop calculating at this point because our KOTH forced the win of a lot of material: capturing the attacker with 1. Qxd8 simply wins a bishop (at least) by complete force. Black has no moves to refute it.
However, for the sake of this exercise let's look at white's other defensive candidate moves.
There are six square the queen can move to in order to escape the attack. However, the bishop on h4 is hanging so any move must either defend the bishop or create a greater threat. The only move that comes close to that is 1. Qd5 (we can reject the other "move" candidates):
White's threat is to capture black's queen. In a more complicated position, we could also apply the same five defensive ideas here to consider how black can best respond to white's threat. But here black's best defensive idea is also to capture the piece, which refutes white's move:
1...Qxd5 2. Rxd5 Bxh4. Now black has two defenders on d8, and can rather simply move his king over, capture the passed pawn, and comfortably be a full bishop ahead. Since this evaluation is much worse than our KOTH, we can reject 1. Qd5.
There are two counterattacking moves that appear to create an equal or greater threat. Let's start with 1. Rd6:
1...Bxg5+ 2. Bxg5 Qxd6. Completely refutes 1. Rd6, so no need to look any further. Since this evaluation is much worse than our current KOTH, we can reject 1. Rd6.
The second counterattacking idea 1. h6:
Is an interesting idea but the "threat" to play the capture-check on g7 is too slow. White's biggest threat is still to capture on d8. So 1. h6 simply allows black to avoid losing his bishop with the defensive idea of pinning the attacker (white's queen) to something of greater value (the king) with:
1...Qxh6 2. Qxh6 gxh6 and now white has lost a pawn (so equal material), and can only initiate equal trades. Now white's d6 pawn will likely be captured. So black need not look any further at defensive replies to h6 since he is now at least equal. Since this evaluation is much worse than white's current KOTH, we can reject 1. h6.
That's it. The goal is to do this calculation in your head in seconds. Many of you probably found Qxd8 in a couple seconds, and did not even consider other replies for white. Or maybe you considered other replies for white first, and then looked at Qxd8 out of desperation. Future positions will be more challenging, I promise!