Before adding the Sezzle checkout button to your cart page, please ensure you've already added Sezzle as a Payment option within Shopify and installed the Sezzle Widget App.
From the Sezzle Widget App within Shopify, go to your cart page and click the toggle on the left that says "Sezzle Checkout Button" until it turns blue to make it appear next to your existing checkout button. Adjust any settings until you get the look and feel and click "Save" at the upper right-hand corner.