Your tablet's Wi-Fi settings are available in the Parent Settings menu under "Device".

In your Parent Settings menu, navigate to Device > Device Settings > Wi-Fi

You will connect to a public Wi-Fi router the same way you connect to a home router.  However one extra step is required if the public Wi-Fi hotspot requires you to agree to their terms and conditions (most do). After establishing a connection to the public Wi-Fi router, launch the Open Browser from the Parents Menu (not the LeapSearch browser).  The Open Browser should open to the Wi-Fi provider's terms and conditions page by default.  On this page, tap the confirmation button to agree to their terms, and then you should be connected to the internet.

Once you connect to the public Wi-Fi router, you will see a check mark and the word "Connected". However, in most cases this only means you are connected to the router, not the internet:

Most public Wi-Fi networks require the user to agree to their terms & conditions in order to access the internet.  To do this, launch the Open Browser from the Parent Settings Home screen.  The Open Browser should open to the internet provider's terms & conditions page.  Once you agree to their terms, you should have internet access. Note: you will not be able to access the internet provider's terms & conditions using the LeapSearch browser on the Kid's page.  You must use the Open Browser in the Parent Settings menu.