Open their profile and choose Follow. Their wishes start showing up in your following feed, so you can see what they've added or changed.

You follow a person, not a single wishlist. And you'll need to be signed in, because guests can't open the following feed.

Only wishes that sit in at least one Public wishlist. Anything in an Invite only or Anyone with the link wishlist stays hidden, even from people who follow you.

The order is by most recent update, not by when a wish was created. An old wish someone just edited can jump back to the top, so it isn't a strict timeline of new things.

Nothing pings you when someone adds a wish. Following doesn't send notifications, so check the feed when you're curious.

There's no way to follow one wishlist on its own. You follow the account and see whatever that person has made public. See "How is my public profile different from sharing a single wishlist?".

You can't follow yourself, so the Follow button never appears on your own profile. And until you follow anyone, the feed just says "No wishes to see here yet! Start following people to see their wishes here."