If you ask a dan player these questions, chances are tsumego will be high on the list. Tsumego helps us learn how to fight. When we understand the vital points of shapes in go, we can not only do damage to our opponent's groups, we can also protect our own groups.
I try to do go problems (I do a mix of tsumego and tesuji problems) every day. About 10-20 minutes in the morning and then whenever I have a few minutes throughout the rest of the day.
For beginners, I highly recommend this set by my good friend Françisa.
I use the following apps for Android:
- Tsumego Pro - Also includes tesuji packs.
- Tsumego - Interesting because you have to play both sides of the problem.
- Go Tesuji - Have to play out both sides of the problem in this app as well.
Personal anecdote: A few months ago I got a review from a dan friend. She told me that my direction of play was quite good, but that I read like a 15k and it was holding me back. Since then, I have dedicated a lot of energy to doing go problems and have seen a definite improvement in my play. My friends at club have even commented on the difference.
You will not see the results right away, but don't be discouraged. It takes time for your mind to absorb the shapes. Stick to it. You will be glad you did.