How do I join my friend family plan after an invite from family sharing ?

Did you follow the links mentioned in the related article to set it up correctly?

Get an Apple Music family subscription - Apple Support

Set up Family Sharing - Apple Support

How to switch to a different subscription plan - Apple Support

Did you also complete these steps?

...

Then follow these steps to subscribe

1. Open the Apple Music app or iTunes.
2. Go to Listen Now or For You.
3. Tap or click the trial offer, (one trial per person or family).
4. Choose Family, then tap or click Start Trial.
5. Sign in with the Apple ID and password that you use to make purchases. If you don’t have an Apple ID, choose Create New Apple ID, then follow the steps. If you're not sure if you have an Apple ID, we can help you find out.
6. Confirm your billing information and add a valid payment method.
7. Tap or click Join.

...

copied from: Get an Apple Music family subscription - Apple Support