One way to transfer assets, especially if it's a scene set up inside Unity, is through the use of Packages. Unity will create a package file which will contain all the assets, scene data and associated meta-data needed to open it in another instance of Unity.
Exporting a Package
- Select all the assets you wish to export inside the Project Panel.
- Go to Assets -> Export Package.
- For convenience sake, make sure the "Include Dependencies" checkbox is checked on.
- Browse through the list and confirm that these are all the assets you wish to export.
- Hit Export and save the package file in a desired location.
Importing a Package
- Go to Assets -> Import Package -> Custom Package.
- Select the package file.
- The contents of the package should show up in the Project Panel.
Important Note: Do all Importing inside of Unity (e.g. don't just double-click the package file). If you don't, Unity will not be able to read the file.