Learn about tiles, z levels, and investigating what an object/unit is (navigation and inspection).
Learn about designations (how to mine, gather plants, chop down trees)
Learn about rooms and workshops (mason, carpenter, bedrooms, dining rooms, offices, walls, doors, grates, stairs, ramps)
Learn about farming (underground preferred)
Learn about trading (crafts, trading depot)
Learn about nobles (bookkeeper and manager to start, followed by broker)
Learn about mechanisms (mechanisms and levers, let power come later)
Learn about military (squads, commanders, fighting, training, equipment)
Explore the rest of the game!
If you want any help, comment or email me in my profile, I would be glad to help!
Why? It's like learning Ruby on Rails with Michael Hartl. You follow his instructions to learn more than just mechanics, but the Rails Way of doing things.
Same with Dwarf Fortress. You need to learn the DF way of doing things, the DF way of solving problems. Easiest way to learn it is to follow deep instruction for a while.
I cannot find the exact tutorial I followed a while ago (and I'm not sure it's even valid for the latest versions) but this wiki ought to help start: http://dwarffortresswiki.org/index.php/DF2014:Quickstart_gui...
Maybe a current DF player can link you to the best multi-year walkthrough :)