This is another one of EVE A to Z's most popular guides. I've expanded and improved it and added even more missioning resources.
A great source of information for missions is the Industrial Sized Knowledge Base. The chapter on missions starts on page 177. Almost everything you'll need is in this book, but I'll include online resources as well. These are nice because you can access them via the in-game browser while you're playing. Here is a site that has some good general information about missions. I also highly recommend this guide on missioning on EVElopedia.
Before you even accept a mission from your agent, you want to see what you're up against. Is this a combat mission, courier mission, or trading mission (hint: you can easily tell which type by the graphic below the mission text)?
Different divisions within each NPC corp give different kinds of missions. You can find this information on page 179 of the ISK book, or on this site.
If it's a trading mission, check prices to make sure it's worth taking the mission.
Remember, unless the mission is a storyline mission, you can safely decline one mission per agent every 4 hours. If you've already declined a mission, you can delay making a decision (for up to 7 days) and take a mission from another agent. Then, after the four hours is up, you can decline the original mission. As far as standing hits go, you're better off declining the mission (even if it involves a standing hit) then you are taking the mission and then either quitting it or not completing it.
If it's a courier mission, take not of the amount of cargo you have to haul and where you have to take it to. Do you have enough cargo capacity on your ship to take it in one trip? If not, how many trips will it take? How many jumps away is the destination? Is the destination in low sec, or does your route take you through low sec? What does the mission pay? Generally speaking, courier missions don't pay very well. However, they're easy, with minimal risk (other than other players). You must weigh all these factors when deciding whether or not to take the mission.
If it's a combat mission, then you want to see what you're up against before making a decision. First, you'll want to check the Mission Reports Guide. This is an excellent tool. You might as well bookmark it in your EVE browser, because you'll be referring to it a lot. The guide lists all the combat missions, sorted by title in alphabetical order. Find your mission on the list and click on it. Now you will see the page for that mission. This will give you some very important information, including:
- What types of damage do the NPC's do? You will want to tank for this damage.
- What types of damage are the NPC's most vulnerable to? If possible, you want to do this type of damage.
- Is the mission in dead space or normal space? If it's in dead space, you can't use a microwarpdrive and you will not be able to warp to the encounter at a range.
- What types of ships will you face, and how many? It will tell you how many rooms and spawns there will be.
- What is the objective? A lot of players get burned in early missions because they think they have to destroy every enemy ship in every mission. Oftentimes, this isn't the case. There is often a mission objective (ie, blowing up a certain ship and taking its cargo), which when completed, completes the missions. In these missions, you can destroy the one ship and get out of there. Also, some players try to do missions as quickly as possible (blitzing). If you want to blitz a mission, then you make a beeline to the objective and don't do anything you don't have to. If you're planning to loot and salvage the mission, though, I recommend you blow up all the ships.
- Miscellaneous information, such as which structures give loot when destroyed (if any), whether or not there are any asteroids for mining, etc.
Be sure to expand and read the player comments, as these are often more helpful than the guide itself.
The ISK book also has some of this information. Pages 183 & 184 give the NPC damage types. Here is an online chart with the same information.
Now you are equipped to kick that mission's ass! Keep it up, and soon you will be a valuable asset to your empire.
Here is a summary list of the resources:
Industrial Sized Knowledgebase. Your EVE manual.
EVElopedia Missions Guide. General missioning information.
Grismar's EVE Wiki. General Mission information.
EVE-Survival Mission Reports. Detailed information on each combat mission.
EVE Geek Mission Types. List of the types of missions different divisions give.
EVElopedia Damage Types. Damage types for NPC factions.