Persons already in the US can change to the H-3 status under certain conditions. The foreign worker must, however, already be holding a valid US visa. This means it is not possible for visa-free travelers to apply for a work permit. The application for a change of status is submitted to the USCIS service center along with the H-3 petition.
Please note that it is not advisable to leave and re-enter the country before your H-3 visa has been approved. The USCIS only approves the H-3 status, it does not issue the visa. This can only be done by the US consulate in your home country. The change of status does NOT mean you have been issued a visa. If you leave the US and try to re-enter without a valid visa, admission into the country will be denied. As opposed to other nonimmigrant visas, the H-3 can also be applied for at US consulates in adjacent countries like Mexico or Canada. Otherwise you usually apply at a US consulate in your home country.