Book your flight to the US. File the I-90 online with USCIS to renew your GC. When you go to the airport for your flight, bring the following --
Your ticket
Your passport
Your expired 10-year GC
A print-out of your I-90 receipt notice downloaded from your USCIS account
A print-out of the CBP memo -- https://www.cbp.gov/sites/default/files/assets/documents/2021-Dec/Reminder- LPR Boarding 20210305.pdf