The AltspaceVR client for Gear VR is now available through the Oculus Store. To download and launch the app, please launch the Oculus App on your phone before you connect your Gear VR.
The easiest way to find the AltspaceVR app is to use the search function, and search 'AltspaceVR'.
Once you've downloaded the app through the Oculus Store, you can find it from then on out in your Library. Follow the menu items for accessing your Library, scroll right to the Apps section and tap Start.
If updates for the AltspaceVR App are released, you may be prompted to update the app prior to launching it.