Contacts can be moved from one organization to another by exporting them from the source organization and then importing them to the destination organization. Follow these steps:

1. Go to the first organization and click on Import/Export tab at the top. Note that this tab may only be visible if you have privileges.

2. Export the Contacts to the CSV file (you can either export all contacts or export some filtered contacts)

3. Now change the organization to the destination organization by clicking on the organization drop down at the top

4. Click on the Import/Export again and this time select Import from CSV file

5. Select the file that you created in step 3 and then map the fields between the csv file and the contact field in the new organization

6. Click on Import

This technique can also be used to import Accounts and Opportunities or for importing from an external file.