Yoga comes in about as many styles as there are teachers. Many yoga studios have low cost new student deals – and several non-profits offer free or donation-based yoga classes on a regular basis. Some classes will be gentle/more restorative, others more dynamic (for instance).
Non-profits offering yoga:
Family Focus (Lawndale)
(and my own community classes in the United Center area and Woodlawn neighborhoods – email me at email@example.com for more info!)