How to copy list from SharePoint 2010 to SharePoint 2013

First go to any list

The choose List in the ribbon

Then list settings

Then save list as template

Then list name

Type what you want

You can include contents if you want

Then go to list template galley do not press ok

Then mark the check box next to the template

And download a copy

Save it to the disk

Then copy it to the sharepoint 2013 server

Then open the home of sharepoint 2013

Go to site settings

Then under web Designer Galleries

List templates

 

Go to files in the Ribbon

Then upload gallery

Then browse choose the document then open

Then save

Then go to the site where you want to add the list

Then site settings
Add app

In the search type then name then search then choose it

Then give it a name and create it