How do i explain my Petty Theft to the Recruiter?

The worst thing you could do in this situation is lie or sugarcoat. Tell the truth to your recruiter, explain what was going on in your life and let them know that you a different person now and want to join the army with the best of intentions. Everyone has made mistakes in their past and if you are open and honest with your recruiter then everything should work out. You didn't commit a terrible crime, you made a mistake and hopefully whatever branch of the Armed Forces you choose will be understanding. Good luck!