I'm new to the game just started a couple days ago and have a some questions. How long does it take to rank up to the next tier? How far can a free player get without spending any money? How does one go about obtaining enough currency (dilithium I think?) to buy the next tier of starship?
Spend your time doing missions, but you can also let your downtime work for you with Duty Officer Assignments. the DOff assignments give items, experience and dilithium while you are asleep or at work.
I set up the max assignments before I go to bed at night, and again before I go to work in the morning. I think about a third of my experience has come from doff assignments.