I am a military spouse stationed in germany, I am an american citizen not currently working , thinking about working part time as a fitness trainer off base. German tax system is, you don't pay tax if you earn not more than 400 euros a month. Question is do I need to claim or right my paycheck to my husbands income tax as a second income? I'm not very good with the tax laws , I need advice about this, please.

The United States expects its citizens to report ALL world-wide income on their income tax returns, so you will report that income earned as a fitness trainer on the joint return you probably will file with your spouse.