There a link to Apple's concierge scheduling service on the Apple Watch page at the online Apple Store, as shown below:
Schedule an Appointment
That takes you to a page where you choose your state and your Apple Store:
Choose Your State
Even though you already chose your store, the next page lists that store plus the nearest stores. Click the “View available times” link, as shown below:
Several Apple Stores
You will then be given blocks of time: Early Morning, Morning, Afternoon, and Evening. These blocks will correspond with your Apple Store's hours. In the example below, there are no Early Morning times.
Blocks of Time
If you click one of those blocks, it will expand to allow you to pick from the available times at that store, as shown below:
Pick a Time
Once you pick the time and confirm it, you will receive an email confirmation. In the opening minutes of this service, many users were timing out, but Apple appears to have got it sorted out. We were able to book appointments at stores in multiple states, and we received confirmation emails for them.
Confirmed