You can gain access to a number of special buffs and bonuses early in the game that will allow you to maximize the experience you get for killing enemies and completing quests and hunts. Completing these tasks give you experience points, but there is a special method involving your rest, camping, and cooking habits that can be combined to provide huge experience point bonuses. When you stay at an inn, you are given an experience points bonus reward on only the experience you have earned so far. This buff does not carry over into the next day like cooking does. Thus, whenever you start a questline or exploration, start your day with a cooking recipe that buffs experience points. The earliest recipe you can get is the multi-meat sandwich that provides 20% extra experience. Raise Ignis' cooking to Level 2 by cooking at campfires, then gather Gighee Ham, Daggerquill Breast, and Aegir Root. Once you have gathered these ingredients, you will unlock the multi-meat sandwich recipe. The ingredients can be found at the following locations:

Gighee Ham: You can purchase this from the shop at Hammerhead. They cost 30 Gil each.

Daggerquill Breast: You can get this from the bird enemies in the far northern part of the first area.

Aegir Root: This is the rarest of the ingredients needed. You can find some near the Vennaugh Haven campground in the southern area of the map. It is found along the road towards the Quay.

Once you have the recipe, go to any campground and camp. Then, cook the multi-meat sandwich. Continue with quests, killing monsters, side quests, and any other activities that reward you with experience points. At the end of the day or whenever you are ready to rest, go to a town and rest at an inn. You can get 1.2x, 1.5x, 2x, etc. experience point bonuses, but it costs more to stay at an inn -- so find a balance that works well for you.

To get 10,000 to 20,000 experience points during a single fight, when you use Elemancy to craft spells, add items listed as coins, such as rare coins. These give an experience points reward if you hit an enemy with it and then kill it. You do not have to kill them with the actual attack. Stack more coins with more powerful spells to improve the effect.