Reserving a gift tells other gift-givers "I've got this one" so two people don't buy the same thing. It doesn't buy the gift, and by default it doesn't spoil the surprise for the wishlist owner.
When you open a wishlist someone shared with you and tap Reserve on a wish, Wishpicks marks that item as taken by you. It quietly keeps gift-givers from overlapping.
Steps
Open the wishlist link the owner shared with you.
Find the wish you want to give.
Tap Reserve on that wish and confirm.
You can optionally add a private note (for example, where you saw it cheaper). This note is only for other gift-givers — the owner never sees it.
Good to know
Reserving is not buying. Wishpicks is not a shop and never takes payment for a gift — after reserving, you still buy the item yourself at the store, usually by tapping the store link on the wish. See "How can someone mark that they will buy a gift?"
The owner doesn't see reservations by default. The "Reveal reservations" setting is off by default, so the owner doesn't even see that anything was reserved. That's what keeps the surprise. See "Can I see if someone reserved my gift?"
One item, one reservation. Once you reserve a wish, no one else can reserve it until the reservation is cancelled. See "Can two people reserve the same gift?"
Reserving doesn't fulfill the wish. Marking a wish as actually received ("fulfilled") is a separate action the owner does later, not something the gift-giver does.
Changed your mind? You can cancel your reservation any time. See "How to cancel a reservation"
Whether you need an account depends on the owner's reservation settings. If reservations are open to anyone (Anonymous Reservations), you can reserve without signing in; if they're limited to registered users (Registered User Reservations), you'll be asked to sign in first. Reserved as a guest and then created an account from that same session? Those reservations carry over. Ones you made on a different device or session won't be linked.