How long can a person travel with a green card?

You can travel within the US with a green card so long as it is valid. A green card is NOT a valid document for international travel outside the US.

To travel outside the US, you will need a passport and possibly visas depending upon the passport you hold and the country you visit.

Please check with the local embassy/consulate for the most up to date visa requirements for your country's passport prior to travel.