After you have been invited to be an immigration trainee, the person who invited you must petition for you via Form I-129, Petition for a Nonimmigrant Worker.  When submitting the form, the petitioner must include all valid evidence demonstrating that the requirements for the visa training program are met by both the H-3 training petitioner and the H-3 trainee.
After USCIS has received the form, you may be asked to take a biometrics exam, if applicable. You will then get a notice of USCIS’s decision telling you whether the petition was accepted or denied. After the petition is approved, you can then apply for the actual H-3 Visa at the U.S. Embassy or consulate.