For Android to Android transferring, a Wi-Fi or 3G/4G connection is not necessary. All you have to do is click the little blue button on the bottom of the screen and have one of the devices create a group. The other Android device will need to also click the little blue button on the bottom of the screen so that it can search for the group. Once both devices are connected to each other, you can freely transfer files between the two Android devices.
View from Android Device(Aaron Yang)
For all of you visual learners out there, here is the official Zapya Android to Android Tutorial. Learn how to transfer files with the best file sharing application out there.