OK, so I'll give a more detailed answer. Orthanc is a vendor neutral archive (aka. a "DICOM server" or a "PACS server without a RIS and without a viewer"):
First of all, you should read the introduction to DICOM in the Orthanc Book:
The operation you want to do (i.e. fetch DICOM images from Orthanc into viewer) is referred to as "query/retrieve". There is a FAQ entry about this topic in the Orthanc Book showing how to configure the Ginkgo CADx viewer against Orthanc:
There is also a video tutorial showing the same with the RadiAnt viewer:
Any DICOM viewer supporting query/retrieve (including Horos/OsiriX) should be configurable in the same way:
For viewers that do not support query/retrieve (there are some of them around), you can download a ZIP file containing one study from Orthanc Explorer. I hope this clarifies things.
Sébastien-