Once you've cleared and started over, it will take you to a screen where you can re-select the product you wish to use (see screenshot) click on the Free button. This will take you to where you can begin entering your information under the free edition of TurboTax.
Depending on what types of forms you need to enter, you may be required to upgrade as you progress through your return, because not all form types and tax situations are included with the free version.