Four years of college- MCAT in that time .. Usually Jr or senior year.
4 Years of med school - after second year do Step I, Step II has various time on when people take it. Some take it before they apply to residencies some wait till after they apply to residencies. Some schools say you need it to graduate others dont. Summer/fall of senior year apply to residencies and do the interview stuff... fairly reminisent of applying to med school.
Start your residency in June... note do not EVER get sick on the first day of June.
An intern is the first year after you graduate that your a resident. It's the year when the rest of the world laughs and mocks you.
Fellowships are done after residencies. Or further down your career if you so wish. They are just extra training in something. So someone could become a pediatrician and then do a fellowship to become a developmental pediatrician.
The match works like the application system to the Texas schools does. You go for an interview at various locations. Then you rank how well you liked each interview. The schools rank how well they liked each applicant. It gets sent to a big computer which arranges it so that the the highest school that you ranked that also liked you is where you get to go.