As others have posted, you can preregister your kiddos 90 days in advance of your stay through the preregistration form on the Aulani website, which allows you to select (iirc) 3 activities. I've read on this forum that you may or may not get all of your 3 choices depending on your length of stay and availability. You don't call to book the complimentary activities (e.g., Aunty's Aloha Party, Stitch's Space Goo, Keiki Hula, Coconut Kings and Queens of Comedy); you do call to book the premium experiences (Fish are Friends and Surf's Up with Chip and Dale).
My wife and I waffled quite a bit whether to sign our kid up for Aunty's Beach House as we weren't sure whether she'd like it. We stayed at Aulani over Christmas week, so when we finally decided all the preregistration spots for the complimentary experiences as well as all spots for the premium experiences were "fully committed."
Notice the distinction.
A CM explained to me that they set aside a certain number of spots for the complimentary experiences for preregistration and leave the remainder for walk ups the day-of the activity. The example she gave me was Stitch's Space Goo had 44 spots filled during preregistration, with 33 spots left for day-of sign up. So I (along with many other parents) ended up waiting in line in front of Aunty's Beach House on the mornings I wanted to sign my kid up for a complimentary activity. Being a busy week, I got in line around 6:40 a.m., but people really started showing up around 7:00 a.m., and the CMs began setting up and taking down names around 7:30-7:40 p.m. You can check the day's activities on Aulani's Daily 'Iwa (newsletter), either online or available from the front desk and concierge after around 10 p.m. the night before.
So if preregistration is filled, you don't get the activities you want, or you want to sign your kid(s) up for more activities than you're preregistered for, walk up is definitely an option. You can sign your kid up for as many activities available that day as you'd like (or think your kid(s) can handle).
For the premium experiences, the CM suggested calling periodically during our stay to see if there were any cancellations. We didn't bother as the complimentary activities were more than enough. I'd also note, if your kid is interested in "surfing" with Chip and Dale like with the premium experience, there's a free ohana (family) activity called Aloha Fun with Disney Friends at the Kipuka Lawn that involves a lot of fun on yoga pad-like "surf boards" and Chip and Dale drop in for about 10 minutes. Again, check the Daily 'Iwa.
A few more things to note.
• Aunty's Beach House offers lunch (grilled cheese and sides) and dinner (macaroni and cheese, pizza, or a burger and sides) for about $8 or $9 (nonrefundable). You do have to line up the morning of to sign up and pay, but this is a nice option if your kid(s) have activities before or after lunch or dinner time, or need to eat in between activities.
• If you completed the registration form during preregistration, you need to fill out only one more form with certain certifications (potty trained, health, etc.) and provide a security word to be used to pick up your kid(s). You will need your kid(s) present to complete the registration, when they take your kid(s)'s picture and issue them a Magic Band. The Magic Band fee is about $14 per band, which is refundable when you return the Magic Band with the original receipt. Your don't have to have your kid(s) with you in line at 7 a.m.. The CMs just ask that you bring them and the form 30 minutes before their first activity to complete registration. Your kid(s) can keep their Magic Band throughout your stay and return it after their last activity or before you check out.
• If your kid is having fun, Aunty's Beach House is happy to have them stay even after their activity has ended, which is nice if you have grown up plans. We signed our kid up for Stitch's Space Goo, Dinner, and Keiki Hula one day, which ran from like 3 to 6:30 p.m. with some breaks in between, and the CM at check-in told us we could pick her up anytime before 9 p.m. However, if your kid wants to leave, they will give you a courtesy call.
Hope this helps!