Path to Grad School? [x-post from r/engineering]

The eventual life goal is to build a skyscraper, and to do that, I need to work for a structural firm, and to do that, it seems that I need to get a Masters in Structural Engineering before (most) large companies will hire (read "consider") me!

So here's the question: How do I get into grad school for engineering?

The majority of advice that I've read on the engineering subreddits talk about the importance of internship over grades to land jobs; is this true for grad schools? i.e. Where does a grad school place its priority of consideration: on grades? internships? research? extra-currics? personality?

Lay your knowledge on me, engineers of reddit!