Updated Sun, Oct 16, 2011 by Space Junkie
Run the tutorial agent missions as soon as possible. Not only will they make you a better EVE player, they will reward you with skills and ships that are very helpful to new players. These tutorial agents can be found under the help button.
As a general rule, you would rather spend your time working on your next mission than salvaging level one or two missions, so you can get faster access to level four missions (where the loot is much better). Don't bother with grabbing every frigate wreck, you'd rather work on that mission grind.
Mission Ship Setups
Need a guide to setting up your mission-running ship? Here are some options:
Level 1 Mission Ships
Level 2 Mission Ships
Level 3 Mission Ships
Level 4 Mission Ships
Other Mission Guides
For more about specific aspects of running missions, check out these EVE mission guides: