Experience is gained upon completing a mission. Generally, missions have a base experience that can be modified up or down by the Game Master depending on how the mission went. If you go on an Araxyte Run and don't run into any Araxytes, you will not get as much experience as someone who ran into and killed the spiders along the way.
Experience per character is determined by dividing the experience gained by your level rounded down to the nearest whole number. So a 100xp mission for a Level 2 character will give them 50% to their next level. A small table can be found below.