I generally have two major outlooks when it comes to an MMO that of the player and of the Player Character (PC). As such (and because I intend to keep them unique), all player related information is italicized and PC will not.
So, welcome to New Eden as I see it, a new player. Eden is HUGE, and can be very hard to grasp in the first few days. So I will start with what I've learned in Eve so far.
1) This game will be overwhelming for the first few days. Be patient and you will learn the rules of space. This game has a 14 and 21 day trial for a reason. Make use of it in understanding the game.
2) There is no levels in the conventional sense. Getting better is based on learning skills and improving them over time (real time. not xp or game time). As such alway be learning a skill and learn long skills (over 8 hours) when you're sleeping/working/at school to get the most out of it. Also, if you switch skills before you finish it will save how far you got and will continue where you left off when you start learning it again.
3) Get a Space-Daddy. Get a friend, a trustworthy Ally, or a helpful starting corporation. Getting someone to help you through the beginning, is infinitely better than trying to figure it out on your own with Rookie Chat as your only life line. In the USNavy (real US Navy), they refer to this coach as a Sea-daddy.
4) Do the Tutorial. Do it. It's there for a reason. If your question could have been explained by the tutorial you will likely be ridiculed. Also, you get a better ship and some decent money doing the tutorial.
5) Don't let yourself get bored. This game is based on what YOU want to do and will not direct you. If you get bored then do something more entertaining.
6) Learn what you want to. The Learning skills increase your speed at learning other things, but is boring. My suggestion is to learn what you want to until you know you like the game. Once you've decided that you want to continue, move to these skills (except charisma) to 3 or 4 (this will take one or two days) then get back to fun stuff. When you're in a cruiser and you have some money (or if your space-daddy is willing to front you some) get the advanced skills and learn them to 3 (4.5M ISK each and two days of learning). Eventually, you'll move them up but these numbers will be excellent for now.
7) You will lose your ship. Maybe not today or tomorrow, but eventually you will lose your ship.
8) Don't fly what you're not willing to lose. If you can't afford to replace your ship. Don't fly it till you can. See #7. Preferably you shouldn't fly what you can't replace five times.
9) "A smart man learns from his mistakes. A wise man learns from the mistakes of others" - Mark Twain. Learn from others mistakes and successes now, before you are presented with the same situation later. http://www.crazykinux.com/2008/06/eve-online-blog-pack.html
10) Have fun. If you aren't having fun, you're playing the game wrong.
1 year ago