Dia. 1
Dia. 1. The stick connection
The stick connection (bo-tsugi) is the initial tesuji. This is a rather uncommon tesuji, so it may be hard to spot. White is now aiming at weaknesses in Black's shape on both the left and the right.

Dia. 2
Dia. 2. The wedge-in tesuji
If Black reinforces his position on the right with 2, White plays two successive wedge-in (warikomi) tesujis with 3 and 5.

Dia. 3
Dia. 3. Black loses the capturing race.
If Black ataries from the outside with 6, White connects at 7 and Black is forced to connect at 8.

White now connects at 9. If Black 10, White 11, and, after the exchange of 12 for 13, Black's stones on the left are caught up in a capturing race in which he is far behind in liberties.

Dia. 4
Dia. 4. Again behind in liberties.
Instead of 6 in Dia. 3, Black might atari on the inside with 6, as in this diagram. After the moves to White 9, Black's stones on the left are again caught up in a capturing race in which they are behind in liberties.

Dia. 5
Dia. 5. A double peep
After White wedges in with 1, Black might atari with 2 and connect with 4. In that case, White will play the double peep of 5.

If Black connects at A, White cuts at B. If Black B, White A.

Dia. 6
Dia. 6. Defending the stones on the left
After White 1 in Dia. 1, if Black secures his stones on the left by making a double bamboo joint with 2, White plays a wedge-in tesuji with 3. If Black 4, the clamp of White 5 is another tesuji.
Next —

Dia. 7
Dia. 7. Short of liberties
Black connects at 6 and White blocks at 7. After the moves to 13, Black can't connect at A because he is short of liberties. Therefore, White can play there, capturing three stones and linking up his group to his stones in the corner.

Dia. 8
Dia. 8. Connect and die
Instead 6 in Dia. 7, the atari of Black 6 here leads to an even bigger loss, as the moves to White 13 show.

If Black connects at the triangled stone, White captures at the circled stone. If Black connects at the circled stone, White captures at the triangled stone. This technique is known in Japanese as oi-otoshi — connect and die.

In conclusion, intuition is not something mysterious that comes into our consciousness from out of the blue or from some unknown realm that inspires us. It comes from a broad knowledge of general principles, shape, and, in particular, tesujis.

Recommended reading
Once you have worked your way through A Survey of the Basic Tesujis, the next book to study is Five Hundred and One Tesuji Problems. This book starts off with a complete list of the 45 standard tesujis. Multiple problems for each are randomly presented throughout the book, just as they would randomly arise in a game. A kyu player who seriously studied these books would gain a lot of facility and flexibility in his or her fighting skills and would surely improve by two or three stones.