MMORPG.com EVE Online Correspondent Tom Yeates writes this article on running missions in EVE Online.

In the beginning...

Allow me to set the scene. You've installed EVE Online; you're on a 14 Day Trial or perhaps you actually own the game and decided to start afresh. Maybe you have dabbled in other aspects of EVE, but you haven't touched any of that "mission stuff". Well, then this article was written for you. It is by no means a definitive guide, but will hopefully provide you some insight into how mission running can benefit your character and your corporation and how to find an agent to get started.

I was like you once... Fresh, brand new and in some ways, overwhelmed by the enormity of the EVE Universe. How do you start off? What do you do? The in-game tutorial guides you through the basic principles of EVE and gifts you rudimentary control over the game interface but it doesn't tell you what to do afterwards. You may be left with a distinct sense that you lack an overbearing aim or a goal. There is no clear cut path, no levels to grind through. You are literally booted into the deep without apology or comment. Welcome to EVE Online.

Read the Mission Running Overview.