How to track google analytics landing page conversions?

For tracking goal conversions from a landing page you would have to first set up goals in google analytics. Goal setting would be the first step you should do when setting up GA for the first time.

For tracking goal conversions from a landing page you would have to create a custom report. This would show goal conversions by landing page and all the goals within it that you want to track on landing page. For this navigate to Customization >> +New Custom Report.  This screenshot will further show the insights of custom reports