Go to the United States Customs line that is meant for foreign nationals when you arrive at an international airport, seaport or any other national port of entry.
Present your green card and your passport to the United States Customs officer who is stationed at that checkpoint. Even after you have received your green card, you need to present your passport as further proof of your identify before exiting or entering the country. Only once you have achieved naturalized U.S. citizenship may you forgo the passport of your country of origin.
Respond to the questions asked to you by the customs officer. The officer asks questions regarding the reason for coming to the U.S., your employment status or about any family you might have in the country. Explain fully the answers to these questions, and get your passport stamped by the officer to proceed entering the country.