I did it, but was living at home with parents (not renting). However I did pay massive amounts in child care (over $300/wk) which would be equivalent to private rental.

Plan every cent. Meal plan, drive plan, play plan.
Only use the car when you have to (or don't have a car at all, public transport is often much cheaper than maintaining a car).
Cook everything from scratch.
Eat vegetarian a few days a week.
Have play dates at the park.
Join the library for books and DVDs.
Freecycle.
Get to know your local op shop.
Go to church - they often have people who are willing and able to help you with $$ and other day to day things.
Don't be afraid to go to a charity if you have to.
Find out what your local Bakers' Delight do with their bread at the end of the day, tell them you're poor and see if they will donate you some.

Good luck. I've bought milk with 5c pieces more times than I care to count.