Applicants for naturalization may file Form N-400, Application for Naturalization, with an expired green card (officially known as a permanent resident card). You are not required by law to apply for a new card. Read more in Apply for Citizenship with an Expired Green Card.
However, if your green card has been lost or stolen, you will need to replace it before filing Form N-400. Use Form I-90, Application to Replace Permanent Resident Card. Approximately 2-3 weeks after filing Form I-90, USCIS will mail you Form I-797, Notice of Action. The Notice of Action is like a receipt that proves you filed Form I-90 successfully. Once you have the Form I-797, Notice of Action, you may file N-400, Application for Naturalization.
At the Oath Ceremony, USCIS will take your green card and provide you with a Certificate of Naturalization, proof of U.S. citizenship.
No credit card or sign up required.