NOTE I:   Make sure that you have all required permissions to Publish template at the SharePoint 2013 site.
NOTE II:  You will need Apps4Rent’s Hosted SharePoint Enterprise Plan to follow these steps.

1. Run the Microsoft InfoPath Designer 2013.
2. Go to the File tab.
3. Click SharePoint Form Library located at the New tab and click Design Form at the right side.
4. You can either create an Infopath template or you could use an exsisting template.
5. Go to the File tab and choose Publish form to a SharePoint Library by clicking at the SharePoint Server icon located at the Publish tab.
6. Type the URL of the SharePoint 2013 site which you have with us.
7. Click Next.
8. Enter your username and password and click OK.
9. Choose the required configuration and click the Next button.
10. Again, you can either choose an existing library to publish your InfoPath template. Or you could create a new library for the publishing your InfoPath template.
11. If you select “Create a new library” then complete the required fields with the name and the description of the new InfoPath library
12. Click the Next button.
13. You can choose to Add columns if needed.
14. Click Publish.
15. Once InfoPath form template is published; click at the Open this form in the browser link and then Close.
16. Click on Save and give a name.
17. You can see your InfoPath template at your SharePoint site.