Go see a recruiter, they will give a list of all the information they need. Make sure to disclose all legal matters upfront. You also need paperwork on any medical issues.
Several case study questions with one or two technical, intelligence, military, or other skill related questions. Questions focused on teamwork, communication, leadership, technical and writing skills. Have examples of professional situations ready.
Interview questions [1]
Question 1
Tell us about a time when you solved a complex issue at work.
I applied in-person. The process took 4 weeks. I interviewed at US Marine Corps (Newark, NJ) in Oct 2018
Interview
There is no real interview to join the Marine Corps. If your recruiter thinks your eligible he/she will do your paperwork for you and send you to MEPs. From there you get medically evaluated and deemed fit/unfit for service.