Facetime isn't working on my MacBook Air. How to fix?

Hi kristafrompotomac

welcome to the Apple (user-to-user) Community!

Re: "Facetime isn't working on my MacBook Air. How to fix? ... FaceTime is asking me to sign in using Apple ID

but when I enter my password the arrow just spins and spins and goes nowhere."

Check you are signed in (to your Mac) with your Apple ID: See: Sign in with your Apple ID - Apple Support

Then see if any of the several tips in Apple Support's online article (link below) can help:

If you can't sign in to your iMessage account or FaceTime on your Mac - Apple Support

Eg: says: "Make sure that the date, time and time zone are correct.

Set the date and time on your Mac"

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Also, if needed: see: If FaceTime isn't working on your Mac - Apple Support

Eg: says: "Make sure you and your recipient have a fast Wi-Fi or mobile connection.

FaceTime calls over Wi-Fi require a broadband connection".

FaceTime Support website (info. / support / contact options etc):

FaceTime - Official Apple Support

All the best :-)