Familiars are obtained by first killing certain monsters to unlock or a group of monster type. After seeing "New Familiar Unlocked in the upper left of the screen you can visit one of the Familiar Stores in Denumald to purchase.
The origins quest must be completed before obtaining familiars. All stores contain the same familiars.
Familiars have a chance to attack each turn, varying from 10 - 50%. Familiars also provide bonuses with varying effects and strength.
Each bonus comes with a upside and downside. eg Pack horse: 5% decrease to equip load (your equipment is lighter) and 10% decrease to dodge chance.
If you are having trouble finding a familiar, you can use the green potion from the potion seller to increase generic encounter rate. When searching for familiars you can use the alchemist form if available to lengthen the potions useable time. Even using these methods is no guarantee to encounter a particular familiar.
To equip new familiars: Go into your inventory, click cosmetics, at the top left click the paw print, scroll through and stop at the familiar you want to use.
Places where familiars can appear are given on the maps above.