How do I masturbate without breaking my hymen?

You do not need to break your hymen to masturbate.  Explore the outside of your 

genital area very gently with your fingers.  You can use a small amount of lubricant 

if you wish.  You will find a great deal of physical pleasure just from self touching like

this.  Your clitoris (you can google this word if you don't know what it is) is a very small

knob between your vaginal lips, high up toward the top.  Touching yourself here will

bring the greatest amount of pleasure.  If you focus on this area for a long time you will

eventually have an orgasm.  How will you know when you have an orgasm?  Trust me.

You will know.

Good luck to you.  You're obviously a healthy young woman.