Combat Experience is gained by killing mobs. XP values displayed on mob pages are averages based on observed values and are a single-player share of the mobs full XP values, divided by the party size the encounter is designed for. Actual values seen in-game may vary considerably from this average due to actual party size and experience modifiers.
Harvesting Experience is received every time you succeed at gathering a resource from a resource node. The experience amount is very small per harvest, but so is the risk to your life. Relax, this experience accumulates over time and can actually be a considerable chunk of your total experience gained. See Harvestables for a listing of all resource nodes and resources. The Resource Node's "Object" page will display the experience gained per harvest.
Crafting Experience is gained, as you might assume, by crafting. Every time you successfully create an item you will receive experience.
Experience can also be gained through PvP combat, but this is very different and goes towards your Abyss Rank rather than your adventuring level. You will also gain Abyss Points, which can be spent, very much like coin, with certain special merchants.