In a city where it often seems absolutely nothing is free, my favorite way to save money is by attending the donation-only yoga sessions at Yoga to the People on St. Marks.
If you come with your own yoga mat, the classes are truly free. I always pay $5 and borrow one of their mats.
There are two floors of classrooms to meet the capacity need and the style is fairly typical vinyasa yoga. No positions are too hard to keep beginners from following along while there's still enough of a challenge to help regulars break a sweat.
Bring water, even in the cold winter, the classrooms can get very warm. There's a small changing area if you don't show up already appropriately dressed but there is no locker room or shower for changing after.