The question is really in the title.
My background in model theory is very limited. Basically nothing past the definition of minimal structures and minimal subsets. I am interested in some strategies that one might use to show that a structure, or a subset of the domain is not minimal.
By minimal I understand: An infinite structure, $A$ is minimal if any subset $Y$ of the domain of $A$, which is definable (with parameters) is either finite or cofinite. A subset $Y \subset A$ is minimal if, for any definable-with-parameters subset $Z$, then $Y \cap Z$ or $Y \setminus Z$ is finite.
Thank you!