How do I apply for a Social Security number after I arrive in the U.S. on a work visa?

If you're authorized to work, apply at a Social Security Administration office (or through the SSN-with-visa option some consulates and USCIS forms offer) using Form SS-5, your passport, visa, I-94, and work-authorization document such as an EAD or an employer letter for H-1B or L-1 holders. There's no fee. It typically takes a couple of weeks after entry for your immigration records to sync, so applying too early can bounce; waiting about ten days after arrival usually works. The card arrives by mail. Your SSN is permanent and unlocks payroll, credit, and most financial accounts. The SSA explains the process for noncitizens at ssa.gov.