Question
when it breaks off how to restart the broke one for replanting.

Answer
Wanda hi!

Did you know an asparagus fern is not really a fern?  It is technically a grass (related to the edible asparagus), that is named a fern due to its resemblance.

Commercially, these are grown from seed.  For the home owner, it would be difficult to save and restart from a broken leaf only.  You could try sticking in a new pot with moist soil and place a bag over it for a few days (until it starts to root), but chances are this would not work.  

Instead, I would recommend breaking off a piece all the way into the ground, including some root mass and some fleshy "tubers" (these are the little fat balls on the roots).  This process is called "division", and it should be very simple and successful.  You can plant this division in a new pot with fresh soil, probably mist for a day or two, and chances are it would grow fresh and new.

Let me know how it did (and thanks for your question)!

DC