There are books about yoga, and many classes that conduct yogic exercises. They can have different slants or ideas behind them. Power yoga and its cousins can be extremely vigorous. Some of the challenging sorts of classes are conducted in especially warm rooms.
I get the impression that many classes are focusing more strongly on a meditation aspect of yoga. In the savasana yogic pose, one usually lies flat out on a mat, much like a corpse would. In that physical position, one relaxes every part of the body that is at all tense and can be relaxed. Some body alignment people suggest a pillow of some sort under the head or behind the knees for greater comfort and posture.
I was nibbling my wife's delicious neck while she was trying to concentrate on some computer work. She said,"Um", which I took to mean I had semi-distracted her as much as she really wanted at that time and it would all right with her if I vacated the very local premises. Sometimes, yoga classes or individual practitioners working at their leisure chant the Sanskrit syllable "Om" . For some, the syllable has special mystical meaning.
Many others are unhappy with too much involvement with Indian, Eastern or ideas or practices from places east of Europe. They are sometimes afraid of punishment from on high for associating with what are perceived as foreign influences.
The evidence for the value of sitting (or lying) still for ten minutes (or even 2 minutes - See "Search Inside Yourself" by the Google official Chade-Meng Tan and the well-known psychologist Daniel Goleman) is steadily mounting. Doing a few stretches and then lying still and concentrating only your breath while dismissing the immediate and important (or trivial) thoughts that try to hook you is valuable, no matter who or what you are.
Time for a new term: YUGA! It is new, totally American, no Sanskrit (or Latin or Greek) involved. You don't even need a class. Lie down, say "Um" softly once (we don't chant much in yuga classes), close your eyes and dismiss each thought that tries to arise until your timer rings.
