EVE is a very interesting game for many players,so here we offer some information about the game to help you play well.
Now that you have been freshly equipped with knowledge of the benefit of mission running - you're hopefully still interested and would like to know how to begin. This is quite a simple process. First you must identify a corporation you wish to work for and a "division" of that corporation. So the logical step here is - what sort of missions do you wish to do? Maybe you're aiming for combat missions in order to rid New Eden of hideous and swarthy, rum loving pirates or something to that effect. Perhaps you are a traveller at heart and seek to run a series of courier missions rather than have your ship put at risk. Alternatively you could be a budding scientist and be seeking R&D agents and their associated missions. Whatever your choice, there is something for you. In all likelihood you will be working for corporations that fall under the umbrella of your chosen race, for example the Caldari State. If not, this doesn't matter. To find out all the corporations within your faction use the "People and Places" search function (set to Faction) and type in your faction's name (Caldari State, Minmatar Republic, Amarr Empire, Gallente Federation) and "Show Info" on that faction. You will find all the corporations within that faction under the "Member Corps" tab.
Obviously there are a lot of corporations here and you are expected to choose only a handful of them. It pays to do your research and good advice would be to seek the highest available quality agent that is relatively close to your start point. Feel free to do some heavy travelling if you decide you dislike the area you are currently in but to save you that time, look around and find an agent that suits you nearby. For example within the Caldari State, corporations like Home Guard and the Caldari Navy have a plethora of agents within reach of the starting stations.