I have been practicing for about 10 years and would strongly recommend taking a "Foundations" class at a local Yoga studio (NOT at a gym or the Y) as a way to start your practice. There is a great potential for injury when postures are done incorrectly. A dozen or so classes with a teacher's supervision will be a valuable investment for the rest of your life.
A few things to consider:
Are you interested in Yoga for physical benefits, psychological benefits, as a spiritual practice or a combination of these?
Although Yoga is a physical practice with an exercise component, it is spiritual practice intended to quiet the mind to allow a person to focus on who they are. The body, mind and spirit are inseparable so Yoga will improve posture and flexibility, both psychologically and physically.
What is your age, weight and overall physical health? Do you have any disabilities?
Hatha Yoga is the umbrella term for all forms of Yoga, but not all forms of Yoga are suitable for all people.
The "Sun Salutation" is a great way to begin a practice at home:
The focus is on the breath, with each movement corresponding to either an inhale or exhale. Do as many repetitions as is comfortable for you (two or three would be a good start).
Practice is traditionally closed by deep relation called Savasana:
Fee free to PM if you would like to discuss this more off line.