These are notes from my first upgrade of SharePoint 2010 to SharePoint 2013. The purpose of the upgrade is to carry out an initial test upgrade to find any issues etc. I’m not replicating the environment in terms of server roles etc. everything is installed on one server with local SQL. I followed the steps outlined here: http://technet.microsoft.com/en-us/library/cc303436.aspx
Copy databases to the new farm for upgrade to SharePoint 2013
As this is a test upgrade, don’t set the databases to read-only.
Backup all the SharePoint 2010 content databases and the databases for any service applications you’re going to upgrade. See part 1 for upgradeable service applications.
Copy the SharePoint 2010 database backups to the SharePoint 2013 SQL server.
Restore the SharePoint 2010 database backups on the SharePoint 2013 SQL server.
If upgrading SQL server versions, change the database compatibility level to match the new SQL server version.