How do I buy extended apple care for my laptop. It expires today

Start here: Check Your Service and Support Coverage - Apple Support. Enter your Mac's serial number on that page and follow the prompts.

Depending on the macOS, the day after it expires you should get a prompt when opening Settings giving the option to extend warranty.

I have an M1 MacBook Air running Sonoma and just a few days ago AppleCare+ expired. The day after I got an email that told me it was expired and to go to Settings and renew it there if I desired. It was a quick processes and no need to go on the web to do it. NOTE that the billing for it will be done automatically to the credit card that you have on file for making Apple purchases.

For me, it didn't take more than a minute or two and when it was done it was only 2-3 minutes later that I received the email with proof of coverage.