Reserving a gift tells other gift-givers "I've got this one," so two people don't turn up with the same thing. It doesn't buy the gift, and by default the owner has no idea it happened.
Steps
Open the wishlist link the owner shared with you.
Find the wish you want to give.
Tap Reserve and confirm.
Add a short note if you like, or skip it.
That's the whole Wishpicks side of it. You still buy the item yourself at the store, usually by tapping the store link on the wish.
Good to know
The owner doesn't see reservations by default. Reveal reservations starts off, so they don't even know something was claimed. That's what keeps the surprise.
Once you reserve a wish, nobody else can reserve it until you cancel. Reserving also doesn't mark the wish as received: that's a separate thing the owner does later, on their side. And if you change your mind, you can cancel any time.
Whether you need an account depends on the owner's settings. With Anonymous Reservations you can reserve without signing in. With Registered User Reservations you'll be asked to sign in first. If you reserved as a guest and then made an account in the same browser, those reservations follow you across. Ones you made on a different browser or device won't.
Related
"How can someone mark that they will buy a gift?"
"Can I see if someone reserved my gift?"
"Can two people reserve the same gift?"
"How to cancel a reservation"
"Can I leave a note when I reserve a gift?"