When you provision a web app in SP2010, you can choose it to use Claims Based Auth or Classic Auth right through the GUI. However, after you have provisioned a web app, there is no GUI to switch from Classic to Claims based. So the below powershell script will let you convert a SP2010 website to claims based auth after it has been provisioned.
1: $w = Get-SPWebApplication "http://sp2010"
2: $w.UseClaimsAuthentication = "True";
The user running the above script should be a member of the SharePoint_Shell_Access role on the config DB, and a member of the WSS_ADMIN_WPG local group.