This is a repository of Useful Links (tm) for players new and old. I've stumbled across a great many Eve sites that help explain various aspects of the game, often far better than I can, so feel free to take a look and learn!
ISK: Industrial Sized Knowledge Base
Probably the single best place to start for new players to Eve. A ton of info you ought to know.
Eve University UniWiki
Love 'em or hate 'em, Eve University's Wiki is another wonderful tool for new players to learn about the game. The Ship Fitting guides near the bottom of the page are a good place for new players to start understanding how to make things work.
2D maps that show a variety of up to date info about what is going on in systems, agents, stations and various other peices of information.
Ombey's Eve in 2D
A more "traditional" pdf based map of Eve, like a road atlas of New Eden.
Mission reports to help you know what to expect, incursion info, and a host of other useful links! I highly recommend setting the mission reports as you in-game browser home page if you plan on running missions as you start out to avoid losing ships to simple mistakes.
Mining and Industry
Halada's Mining Guide PDF Wiki
If you want to mine, start and finish learning with this.
Eve Dev Equations
chrucker Eve Math
Jester's Trek Fit of the Week (FOTW)
Usually interesting thoughts on various ways to use and/or tweak ships.
Eve Battleclinic Loadouts
Probably the largest online repository of fits online, with the added fun of a comments section! Use these fits at your own risk.
E-Uni Ship & Skill Guides
Amarr - Caldari - Gallente - Minmatar - ORE (Mining/Salvaging)
Some basic fits that you can learn from, sorted by race. Not bad for starting to figure things out, and gives recommended skill training to go with the fits to make them effective.
Use this. Learn to use this. Just do it. It can track almost anything in the game, store, import and export ship fits, manage production, research, invention, look up WH info, plan routes, manage a POS, and other stuff too.
The "Barebones" ship fitting tool, compared to EHQ.
Fitting tool that runs on Macs and Linux, if you need that. The least featured, but at least you can use it!