How to sign up and activate an Apple Music family plan

Apple Music's family plan is hooked into iOS and OS X's Family Sharing feature: It lets multiple different Apple IDs share calendars, photos, movies, TV, and music. Previous to Family Sharing, families had to use one Apple ID for all their purchases—which can be a pain on a number of levels. When you sign up for an Apple Music Family plan, which supports simultaneous listening for up to six devices or accounts, all the infrastructure is being taken care of by Family Sharing. In theory, getting your family on board is as simple as signing up for Family Sharing, purchasing a Family subscription, and having your other family members log in.

How to sign up for Apple Music's family plan

Note: If your family members have already signed up for an Apple Music free trial, this won't work; you'll have to wait until after their free trial period is over to sign them up as part of your Family plan.

Set up a Family Sharing account, if you haven't already, and invite the people you'd like to share your Apple Music subscription with.
Sign up for Apple Music with the administrator of your Family Sharing account, and choose Family when prompted to sign up for a plan. (If you've already chosen the Individual plan, you can change this by tapping the Account icon in the upper left corner of the Music app, then going to View Apple ID > Manage > Subscriptions > Apple Music Membership.)
On your family member's device, make sure their account is signed in for both iCloud and iTunes in Settings > iCloud and Settings > iTunes & App Store.
Open the Music app and tap Already a member? at the bottom of the Apple Music signup sheet (or tap the Account icon) and sign in with that family member's Apple ID. Do not register for a free trial on that family member's device.
Assuming everything goes according to plan, you'll see the "Your family has joined Apple Music." screen and an option to enable iCloud Music Library.