To export a test case or set of test cases from the current project to another project in the system, all you need to do is select the check-boxes of the test case(s) you want to export and then click Tools > Export Tests. This will then bring up a list of possible destination projects:
Once you have chosen the destination project and clicked the <Export> button, the test cases will be exported from the current project to the destination project. Any file attachments will also be copied to the destination project along with the test cases.