Gryfa live in the Shattered Lands, mostly on the larger islands, either in caves or trees. Actual dwellings range from a simple pallet on the cave floor, to elaborate tree-house-like 'nests'. Their society is very tribal, with a hereditary chieftain, medicine persons, warriors, hunters, and gatherers. Gryfon young learn the ways of the tribe by watching and helping, not in a formal school. They live mostly off hunted game (land, water, and air). Nobody (except maybe a Gryfophobe) likes to talk about it very much, but occasional tribes do make it a practice to eat slain enemies.
A Gryfon's life revolves around the hunt, and occasionally, the raid. They raid mostly to obtain things they don't have, like grain, tools, or wives. These raids are highly stylized, more like trading parties. They bring payments, but a fight usually takes place. If the raid is on a neighboring tribe of Gryfon, the fight is limited to counting coup, but if they decide that a Sphynx village (or some other species) is withholding trade, or has given some other offense, things can get deadly.
Gryfon don't really like Sphynx because they don't like Gryfon, and come across as 'very snooty'.
A character who's player decides it should be a Gryfon will need to be in one of these classes; Cleric, Fighter, Thief, Psionic, any two, or any three. (But not a Cleric/Thief.)
By their nature, Gryfon are non-magical and never use magical spells (not counting clerical spells). This gives a bonus to their saving throws against attacks from magical wands, staves, and rods, and spells. This bonus is +1 for every 3? points of constitution score. (see Table 9 in the PH)
Gryfon also suffer a 20 percent chance for failure every time they try to use a magical item not suited to their particular class. (See dwarves on page 21 in the PH for details.)
Gryfon, having practiced a great deal as fledglings, get a +1 bonus on attack rolls for spear, quarter-staff, and staff sling. (They generally use a single weapon that does all three, but they need to spend a proficiency slot for each way they want to use it, so as not to incur a penalty).
Gryfa have 60 foot infravision.
When considering wild psionic talents, Gryfa are allowed a +1 to their base chance, which is then multiplied by three. If this roll is not successful, the Gryfon character may still get racial psionics. If the check roll was 10 or under, he will have a levitational power, and if between 11 and 15, inclusive, teleportation.
Even though a Gryfon has wings, he cannot fly. He is too heavy for his wingspan. He is able to glide, although exactly how far is dependant on local conditions. He does get enough lift to gain seven points of movement when running. If he uses this speed in a charge, he get a +1 to damage and a -1 to attack.
Gryfa subtract 1 from their intelligences, since they sort of don't really care what it is that makes things happen, or how it works. Since that they have wings to use as a balance bar, Gryfa get 1 additional point of dexterity.