How do I connect the standard sign-up pop-up that comes with Shopify to Klaviyo?

First, go to Integrations > Shopify. Now from the drop-down list, pick the subscriber customers integrated with your Klaviyo marketing list. This technique should work, and your emails will become visible in Klaviyo. If it doesn't, try replacing the Form Action URL with the subscribe page URL for your Klaviyo list.