|Adventures of an EVE Online Newb||
To get missions, you have to go to agents which may or may not like you (good/bad standing) and you may not be at their level. You can search for agents using the EVE Agent Finder or the in-game Agent Finder. The only problem I'm having so far is that the filtering sucks; you have to scroll through long lists of regions/star-systems or whatever else to be able to filter out agents.
Sometimes I just pick up whatever missions are around in an area. The nice thing about missions is that their time limit is usually long enough that you don't have to worry much and can take a break after you accept a whole bunch of missions. The other nice thing is that you'll eventually get missions with big payouts (1mil+). When I have to study what I do is pick up missions, study for 30min, do the mission in less than 10min and then go back to studying. Having drones and fleetmates helps finish missions even more quickly (drones don't help as much as I would want because they aren't fully automatic...).
(Update: Grismar's EVE Wiki is out of date, try and stick to the official EVE wiki I guess?) Grismar's EVE wiki has a section about agent levels and qualities. You need destroyers or crusiers for level 2 missions. According to that wiki, level 4 missions absolutely require 2+ people. The agent quality determines how close the missions will be to your current system and how hard and rewarding the mission is. If the mission is harder you will get a bigger payout and hopefully you won't have to jump too many systems away to complete it either!
I'm flying a Thorax right now and it is a Gallente tech 1 cruiser which means I can easily finish level 1 missions, and I'll be able to do level 2 missions though not as easily as I would like (this is why I've been focusing on improving my DPS heh).