Which version of ADS are you using? The process is different for ADS 2009U1 and earlier compared to ADS 2011.01 or later. I can guess perhaps that you are using an older version, ADS 2009U1 or earlier, as you are referring to projects rether than workspaces but would need to know this for sure.
Firstly, I would really suggest that you upgrade to a later version of ADS. ADS 2008 is six years old now and obsolete. Newer vesrions like ADS 2012 or ADS 2013 are far more capable and are built on a library structure that is designed to make sharing design data between workspace and users far simpler.
It is not exactly the same but you can do similar things in ADS 2008 using the project include feature. This makes all designs that were created in one project available for use in another project. So start ADS and open the project were you wish to use the design data. Then in the main window select the Files > Include/Remove Projects... menu function. In the window that opens use the left File Browser panel to navigate to and select the project that contains the design that you wish to reuse and select the button to >> Include >> that project in the current Project Hierarchy list and OK out of the command. All the designs from the included project are now usable in the current proect just like designs from that project itself. The designs do not need to be copied to be able to be reused.
If you do require a copy of the design so that it can be edited and changed from the original in the current project simply open that design and use the Save As function to create a new copy in the current project. The advantage of this is that you now have the new copy that can be modified as required but also the original design is still available in the included project as a reference to be use as necessary.
If you no longer required the included project you can go back to the Include/Remove Projects... command and << Remove << the project from the Project Hierarchy list.
I found an easy way for the above issue. I convert to a template the design which I want to transfer to another project. Then I can access this template from everywhere.