[kingant]

Bit of a generic answer.

Doing the problem sets from a good university course.

Some problems might take you hours to solve, but it will develop your stamina for thinking hard.

[curious16]

Any particular set of courses you have in mind?

[kingant]

Sure for mathematical problem solving skills, here is a good one: http://people.csail.mit.edu/moitra/854.html.

It requires minimal mathematical background (undergraduate level discrete math). But you will learn a bunch of relevant algorithmic concepts. And the problem sets are hard!