"Find Familiar" is no longer a spell, it is a class feature that Druids, Sorcerers, and Wizards all get at 2nd level. Why druids? Because one of my players asked if their druid could have a familiar, and I couldn't think of a compelling reason why not.
The caster chooses the familiar they want, from a special list prepared by the DM. (Why are squirrels on the list? Because one of my players asked for one, and I couldn't think of a compelling reason to say no.) This choice is sorta-permanent; it can be changed later by completing a 24-hour ritual (that consumes 100gp worth of components). But the first one's free.
While their familiar occupies the same space as the caster, they get a minor bonus. My list is below, cribbed from the 3.5E PHB:
- Bat: caster gains Blindsight to a range of 10'. If the caster already has Blindsight, the range increases by 10'.
- Cat: caster gains Advantage on Dexterity (Stealth) checks. (In the past, I've had a player ask if they could swap out "takes half damage from falling" instead of Stealth, "because cats always land on their feet." I thought that was a cool idea so I allowed it.)
- Hawk: caster has Advantage on Wisdom (Perception) rolls involving sight
- Lizard: caster gains a Climb speed of 10'. If the caster already has a climb speed, that speed increases by 10'.
- Owl: caster gains Darkvision to a range of 60'. If the caster already has Darkvision, the range increases by 60'.
- Rat: caster has Advantage on Constitution saving throws.
- Raven: caster can speak and understand one additional language of their choice.
- Snake: caster gains Advantage on Charisma (Deception) checks.
- Squirrel: caster gains Advantage on Dexterity (Acrobatics) checks.
- Toad: caster gains a Swim speed of 10'. If the caster already has a swim speed, that speed increases by 10'.
- Weasel: caster gains Advantage on Dexterity save throws.
The familiar is an NPC with its own character sheet...it's basically the stats for the creature in the Monster Manual, but with the following changes. (These changes were also cribbed/adapted from the 3.5E PHB. The stats for squirrel are homebrew.) It uses the caster's initiative, and acts immediately after the caster in the turn order.
Hit Dice: the HD of the creature is equal to the caster's level.
Hit Points: always 1/2 the caster's total hit points.
Attacks: the familiar's attack rolls use the caster's spell attack bonus
Save throws: the familiar adds the caster's proficiency bonus to all save throws.
Familiar Abilities: both the familiar and the caster gain the Alert feat whenever they occupy the same space. The caster can communicate telepathically with the familiar to a range of 100 feet, and can see what it sees and hear what it hears (but is blind/deaf during this time). The familiar can deliver touch spells to a range of 100 feet.