Stats listed in the find familiar spell description are used. Stats not provided are taken from a monster book.
Often, stats for a familiar are found in the MM2, rather than the MM. Rules listed under find familiar always trump the monster books.
Abilities listed in the books which are conferred to the character are vague, and are expanded on as follows.Ex
VERY rough draft. Only some of these are in use so far. They need work.
Cat, black
Surprise 1-in-6: Party only surprised on a 1-in-6 (does not stack with ranger or monk ability).
Regular encounter distance in the dark: Spot enemies at the normal encounter distance, even in the dark, as long as there as a little light (even as dark as a new moon).
Low-light spotting: Negate effects that hamper vision due to low light. DM will also increase chance to notice things in a dungeon if the chance of noticing them would be aided by low-light vision.
Crow
Fly to increase encounter distance 3x: Outdoors, fly to multiply encounter distance by 3x. Doesn't work (1) in medium woods or thicker, (2) if there is heavy precipitation, or (3) if the crow is surprised. (The crow provides a special surprise check which happens before the party's check.)
Daytime vision 3x: 3x vision distance outdoors during daytime. (Does not affect encounter distance, just lets character see farther.)
Small movement spotting: DM provides better chance to notice things that involve small movements (e.g. may provide bonus to notice a trap)
Hawk
Never surprised if vision matters: Party is never surprised unless vision is irrelevant to the scenario (e.g. opening a door).
1)
Fly to increase encounter distance 10x: Outdoors, can fly to multiply encounter distance by 10x. Doesn't work (1) in medium woods or thicker, (2) if there is heavy precipitation, or (3) if the hawk is somehow surprised.
Daytime vision 10x: 10x vision distance outdoors during daytime. (Does not affect encounter distance, just lets character see farther.)
Owl, screech
Never surprised dusk or dark: Party is never surprised during dusk or darkness.
2)
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Toad
Weasel
Surprise 1-in-6 if sound or smell matters: Party only surprised on a 1-in-6 when sound or strong smell is a factor (does not stack with ranger or monk ability).
Scent: Character is able to pick up on smells that would be undetectable by normal creatures, possibly providing valuable information.
Remember that these sensory abilities are imparted to their master. The master does not need to ask the familiar what they see/hear. The master sees/hears themselves.
The player should endeavor to remind the DM of their special abilities when they believe the abilities might be relevant, as the DM can easily forget about a familiar.