How do you feed fish to yourself in Torchlight? I know how to do feed it to my pet but not myself.
Most common fish are for pet consumption.
Other loot to be had from fishing holes includes random armor, health/mana food (essentially pots), and those that give various defensive buffs (elemental resistances, armor, knockback resist, etc).
Fish can only be fed to your pet. http://www.runicfollower.com/wiki/torchlight/Fish
The Wiki at wikia states it as followed:
Fish are consumable items for pets, acquired through trading and fishing. Fish may temporarily transform your pet into a monster, permanently transform your pet into another type of pet, or give it straight boosts to specific properties for a limited period of time. Fish may also contain items of any rarity (all the way up to Unique) and consumables for the player.
At the bottom of the page there also is a list of Player Consumable Fish
As stated by C Ross in his comment, this type of "fish" shows up in the equipment tab and is consumed via simple Right-click: