How can one use the earth as a second wire?
Your assumption is based on the fact that all voltages are referred to a "common" ground. But that's not true!

The voltage is also called "electric potential difference"; note the word "difference".

This means that a "3V voltage" means nothing; you should specify with respect to what. In your case a "3V voltage" battery is a battery whose + terminal has an electric potential 3V higher than its - terminal. If you try to measure the voltage between either of its terminals and the ground, without making any connections, you will always read 0V.

That's why you can put batteries in series to get a higher voltage.