Hi,
You probably want to configure the HikaShop cart notification plugin via the Joomla plugins manager.
There, you'll find several settings to configure the behavior of HikaShop after a product is added to the cart.
By default, it will just display a notification box on the corner of the page, but you can configure it to display a popup with a button to access the checkout, or have it redirect the customer directly to the checkout.
You can also create a menu item of the type "HikaShop checkout" via the Joomla menu manager so that the customer can click on that menu item to access the checkout when his cart is not empty.
Regarding Square, once you have it installed, you can go in the System>Payment methods menu of the HikaShop backend. There, click on the "new" button and select the square plugin. You'll then see the settings of the Square plugin that you have to fill in.