MAAK holds the official breed standard in Russian, but also has an English translation, here is an excerpt:

Description of characteristic type and exterior of Akhal-Teke horse

Head: light, dry with wide lean lower jaw, straight profile or with convex forehead, prolonged facial part; big eyes with special slanting shape (slant-eyed) and overhanging superciliary arches; thin, mobile, high set up ears; thin lips and nostrils; long, wide poll.
The head is set on the neck at acute angle.

Neck: high set, long, straight or S-arched, round in cross-section, flexible.

Body:
The withers: high, long, well-muscled.
The shoulder: long, slant set, with well-developed muscles
The upper arm: with normal slope, well-muscled
The chest: deep, wider behind shoulders, oval form, with long false ribs.
The back and loins: even, relatively wide, may be with some insignificant lengthiness
The croup: with normal slope, sometime a bit slopping, wide, long, and with strong muscles lowering well down to gaskin.
The tail: low and deep set, often practically hair-less at the dock

Legs: lean, long with well-developed joints and firm well-shown tendons, small strongly built hooves. The legs stand parallel to each other, feather are absence or very insignificantly present.

Muscles: flat, dense with long fibers

Coat: thin, silky, light main and tail, forelock and feather are absent or insignificantly present.

Movements: spacey, flexible, elastic, with good impulse, comfortable for rider at all gates; strong, flexible jump at flat trajectory and good style.

Colors: big variety of colors from black to cream, often with typical metallic shine – golden and silver.
Expressed markings/spots could be met, similar to tobiano.

More information about the breed standard from MAAK in Russian

There is no other horse that leaves such unforgettable impression as the noble Akhal-Teke – lithe, light and springy, glistening with gold in the rays of the sun, with its smooth gliding trot and a ground-lining gallop. (A. Klimuk)

Additional information about Akhal-Tekes and how they look and are classified from other organizations:
Akahl-Teke Association of America breed standard
Conformation from the Czech Achal Teke Association
The Akhal-Téké horse – Description by Akhal-Teke France

Although a breed standard is important, many breeders prefer to select their horses by performance goals, such as at the racetrack as well as in endurance racing, jumping and dressage. Halter gradings are important, but each horse’s conformation will vary with their purpose, and breeding goals take this into consideration.

A note on Lines & Types:
Dr. Mihail Ivanovitch Belonogoff, a colleague of Dr. Riabova’s, had classified the Akhal-Tekes as light, medium and massive, however Dr. Riabova has stated the classification system is too primitive to adequately describe the diversity that actually exists in the many Akhal-Teke lines. Currently the breed is represented by 18 different sire lines and is represented throughout the world, still largely in Asia, but spreading to Japan and China, Australia, Europe and North America.

The Akhal-Teke is an elegant, exotic animal exuding grace, power and athleticism. The comparison in appearance to a cheetah or fine greyhound is not inaccurate. (ATAA)