When trying to improve one's level of play in Go, it is often considered importent to learn to see the resolution of a given position with one look. To that effect, it is helpful to study tsumego.
The word tsumego means "filling the stones". This should be read as finding the one solution of a mostly local problem. Fuseki or chuban problems are problems where several options exist, and thus not tsumego. The most typical tsumego is the Life and Death tsumego, where the goal is to find the one way to kill or save a given group, or to see if there is no such move. Other examples include connection tsumego and ladder tsumego. Solving tsumego often requires a tesuji, i.e. a clever move.
As the study of tsumego is considered vital for improvement in Go, there is a wide variety of books devoted entirely to them, ranked by difficulty. In the weekly go hour on NHK, there is also a tsumego section, with one problem every week.
Usually one tries to solve a problem after the other, not looking at the solution before being absolutely sure the found solution is correct. When solving tsumego, there are two approaches:
1.) Solve it fast, on sight, or
2.) Try to read out the entire situation, with every possible move and countermove, until you are sure you know the right solution
There are also a number of webpages providing new tsumego regularly: