What is dimensional analysis and how is it used?

When one is faced with a problem requiring derivation of an equation, they might be asked to use dimensional analysis. This is a concept that involves analyzing the units of known quantities (usually it is easy to work in SI, one could work out these base quantities like mass in kg, distance in m, time in s, etc. by using more basic known equations) using the fact that any physically meaningful equation has the same dimensions (units, factors) on the left and the right side.