The first thing, which young tester should worry about is the mind training, that should help to solve the problems. It is much more easier solve the problem when you know how to start and which steps to do next (especially, when you work at the support and need to solve the particular problem with known result but unknown steps). And the best way to train mind is to play games.
Famous Bulls and Cows is the good game for the beginning. It helps to find your own method in finding the right answer. Classical rules are simple: there is 4 digit number which you should guess. Number may not begin with 0 and all digits should be different. If in the proposed number there is right digit in the right place - it is a bull, if there is right digit in the wrong place - it is a cow. For example, if the right number is 3268 and the proposed number is 1234, then there is 1 cow (3) and 1 bull (2). The most intettesting part is that any number can be guessed in 7 tries or less. Which means, that there exist a method which you should apply for solving this kind of problems.
There is a lot of online games which you can play. For example, I like http://5ko.free.fr/en/bk.html because there is an ooportunity to make some notes (digits that are not in the number for sure).
So the goal is to train yourself to guess any number in at least 7 tries. And the next step is to make the time limit (guess any number in at least 7 tries and in 10 minutes).