Mission Running

Since this is my first post in the series about the kinds of activities I do in EVE (what I'll be calling my "confessions"), a note: I'll cover all the basics of how to go about doing it, but not in particularly great depth as there are generally much better how-to guides out there. I'll link any of those I've found useful. Instead I'll spend most of my time talking about the "why" - why it is I do this part of the game, why I take enjoyment out of it, why I'm repping for the people who do these kinds of activities and get tarnished with the label "carebear" for it.

The What 

Mission running is one of the most basic Player Vs Environment (PVE) activities in EVE, starting with the tutorial missions that introduce the player to the game mechanics and give you your first ships. You dock your ship in a station owned by an NPC corporation. Agents of that corporation offer you a mission, generally involving flying somewhere, doing something (blowing up pirates (rats), mining ice or asteroids (roids), couriering an item), and coming back when you've completed the objectives for your reward. The more missions you do with a particular corp the higher your standing with them gets - and as your standing grows, more agents and better missions become available to you.
 

The Where

Anywhere there's an NPC station there's generally some sort of agents available. Players tend to concentrate their efforts in "mission hubs", though, where several high-level agents of the same type are available in close proximity, so if one gives you a bad mission you can move onto another.

The How

As always, the best place to study the mechanics is Eve Uni Wiki's page on the topic. The majority of mission running, particularly at the high end, is done for Security agents, and involved blowing up a deadspace pocket(s) full of rats for the bounty on their heads, the salvage you can take from their wrecks, and the ISK and corporation Loyalty Points (LP) you get given for completing the mission.

A few notes:

• always check the mission out on Eve Survival. Their search function can be screwy so I usually end up googling the mission name, faction and level to get the details. They catalogue exactly what kind of damage will be done by who as well as giving handy tips on managing aggression and how to blitz the mission if that's your goal.
• I've only recently started using a Mobile Tractor Unit. This is a noobish thing to admit, but whatever. As soon as you can afford to buy one, do it; definitely by the time you are running level 3 missions. Pop it down as soon as you enter the pocket and as you're blowing stuff up it's hauling it in and stripping it of modules, allowing you to get right to the business of salvaging the wrecks once you're done blowing everything up. SUCH a timesaver.
• Flying in a fleet is great when you are starting level 4s, especially if you're only skilled to BattleCruiser level or only just got into a Battleship. I lost my first Dominix to lowly NPC rats flying solo; having a more experienced player along for the ride meant I wasn't riding on the edge of my tank. 
• That being said, once you've trained the skills and got the procedures down to comfortably solo a L4 mission, you probably lose ISK flying in a fleet compared to what you could be making doing it yourself - unless the fleet is well organised with a dedicated salvager and logi. 

The Why

Mission running is a pretty basic form of PVE activity in EVE, but after two years of running level 4s it's still fun to crack your knuckles, warp in on the bonus room of Angel Extravaganza, and let rip on a whole fleet of rats. Plus there's something fun about tinkering with a fit, or coming up with a new one, and trying things a little differently. If you're after something a little more challenging, there's the Epic Arc missions - once you get standing to 5 with a faction you get access to this narrative-driven series of missions, generally tougher than their equivalent level. Another option for a challenge is the recently introduced burner missions - a special type where you can only fly frigates, and will face a single enemy with the equivalent fit and skills of another player. I'm yet to do one!

Why spend time mission running: it's pretty safe ISK, good reliable isk per hour, and more fun than putting lasers on rocks. Plus it's pretty much the only way to increase your faction standings, which come in handy for things like refining and sales.

Why not: once you've run the same mission a few times over they can get pretty tedious, and it's also not the most lucrative PVE activity by far. For me it's a staple; when our corp isn't at war I like to put in a good couple of hours of solo missioning, plus our corp's once weekly mission fleet, as a minimum. But once I've done that I'm usually looking for another way to make the ISK.

Mission "griefing" - hostile players warping in on your deadspace and taking your kills/attacking you - isn't that common in high sec space. Although it does happen, it's only occured to me once in several years - so much less so than miner ganking,. However a good l4 mission fit is a more expensive boat to risk than a miner and requires more skill points to fly well (in a coming post I'll link my normal Dominix fit and discuss some tactics). There's no such thing as risk-free ISK in EVE, but the risk for missioning is minimal.

Despite the above considerations, I think missions are a great fleet activity. They are a good way for newbies to cut their teeth on the procedures of flying in a fleet, as well as for the vets to help newbies turn in for higher level rewards quicker than they'd make on their own, and a way to make some ISK while having a laugh - I'll never forget two corpies starting a duel over the 10m3 of Quafe needed to complete a mission! For us, a corp of mostly high sec care bears who dip our toes into other areas, Mission Mondays is a common denominator.