An After Effects Project file (and a Premiere Pro project file) only contains links to the source footage. You can use the File menu to consolidate and create copies of the original footage in a separate folder, but there is no way to share an AEP or a Premiere project without also sharing the original source footage (files).
You can consolidate, so that unused footage is not shared, but even if you only use one layer in a 100 layer PSD file, the original PSD file must be shared.
With many of my Clients I use Dropbox to store the original source files so they have easy access. With some, I use Google Drive. With others, we use proprietary file-sharing systems, so that transfer times and uploads are minimized.
I hope this helps. Just start by selecting the master Comp in the Project Panel then go to File/Dependencies and choose carefully and read the options. Often the first menu option is all that is needed. You will end up being asked to select a location to save the new AEP, and a Footage folder will be created with copies of the required footage.