How to move Lists/Libraries from one Site Collection to another Site Collection?

Moving Lists/Libraries can be acheived either using 'Save as template' option or 'Import/Export' commands.

Using Save as template:

1. Create a List in source Site Collection .
2. From the Ribbon (Feature available in Sharepoint 2010) , Select List Settings
3. Click on the link Save List as Template.
4. Assign a Name , Description to the template, Select the checkbox for 'Include Content' (if we really want to move content along with the schema).
5. Click ok , which displays a message saying template is available in List Templates gallery.
6. Go to 'Site Actions' in the top level site ->Site Settings-> Under Galleries section , click on List Templates, where we find the created template. click on the template file where it will ask us to save.Choose the appropriate location to save the template on the computer.
7. Go to target Site Collection.
8. Go to Site Actions -> Site Settings -> Under Galleries section, click on List Templates
9. From the Ribbon, click 'Upload Document' , choose the template file which we saved earlier on computer.
10. Once the template is uploaded, it will available in the List template gallery when we create a new list.Coose that to create a new list.

Follow the same procedure to move Libraries and also Sites, but when we save Site as template , the template created will be available in Solutions Gallery.

Note: List/Library when saved as template , it save with extension .stp. Site when saved as template, it saves with extension .wsp.

Using Import/Export Commands to move Site::

Open Sharepoint 2010 Management Console.

Export a Site: Export-SPWeb -identity 'Url of the site to move' -path 'Path of the .dat file to store'
     Ex:    Export-SPWeb -identity 'http://test/sites/teamsite' -path 'c:\temp.dat'

Import a Site: Import-SPWeb -identity 'Url of the target location' -path 'Path of the .dat file to retrive site '
    Ex:     Import-SPWeb -identity 'http://test/sites/targetteamsite' -path 'c:\temp.dat'

Note: Before moving site to target location, make sure the target site is of same template and also check the fetures activated in source are also activated in target site to avoid unexpected Issues/Exceptions.