I started last summer, because I had no $$ yet for a gym membership. I'd just start walking, and then say "OK self, run to that street sign there." Gradually, I'd go for longer distances, and eventually phased out the walking.
I got so into it, and enjoyed the challenge so much that I signed up for (and finished) a 5k back in November. I'm doing my first 8k in April!
For me, running races gives me a goal to work toward and gives me such a feeling of accomplishment, even if I finish dead last.
Yay for running! Just remember, slow & steady wins the race