If there is a new moon every month, where does the old one go?

We have only one moon. the new moon means a full moon.
the shapes of the moon are different because of the way the sun hits it.

hope this answers your question!

It is the same moon, the moon is the same throughout all phases. "new moon" is the name of the phase where no sunlight is reflecting off the moon. 

the phase of the moon when it is in conjunction with the sun and invisible from earth, or shortly thereafter when it appears as a slender crescent.

An atom that has fewer electrons that protons is called a positive ion.