To change the shipping settings, from the store dashboard go to:
> Store Settings > Checkout > Shipping

From within this page, the headings containing 'Free shipping', 'Super Savings shipping', 'Standard shipping' and 'Expedited shipping' are all separate shipping methods which can be individually altered to your liking.
To enable/disable a specific shipping method, check/uncheck its corresponding tick-box labelled 'Enable this option':

For the 'Free shipping' method only, you can 'Enable only if order is at least' over a certain price. For example, if this setting was set to $10, and the total of the basket came to $8.99, then 'Free shipping' would not become available:

The 'Title' and 'Shipping Time' for each shipping method can also be edited and set to how you wish.
To alter the shipping settings only for specific product categories, please see this guide.
(*Don't forget to click 'Save Changes' after making alterations*)