An analogy question gives one pair with a hidden relationship and asks you to complete a second pair with the same relationship. The fastest method is to put the first relationship into a short sentence before looking at the options: "a pen is the tool a writer uses", or "the second number is the cube of the first". Then test that sentence on the second pair. If it fits only one option, you are done. If it fits several, make the sentence more precise.
The questions come in three families: word analogies, number analogies and letter analogies. Each has a small set of relationships that appears again and again, so learning them turns most questions into recognition rather than search.