Once you've signed in, tap Follow on someone's profile, and the wishes on their lists set to Everyone show up on Home under From people you follow.
You follow people, not lists, starting from their profile link or a list they've shared. Your own profile has no Follow button.
Steps
Sign in. Without an account, tapping Follow shows "Sign in to follow people".
Open their profile: tap their name on a list they've shared with you, or open the profile link they sent.
Tap Follow. It changes to Following, and you'll see "You're now following" with their name. If they already follow you, the button reads Follow back.
Go to Home. Their wishes on lists set to Everyone, old and new, show under From people you follow, most recently added or changed first. Tap See all if there are more than fit. No section there? Nobody you follow has a wish on a list set to Everyone yet.
Will they know I followed them?
No, they don't get an email or anything in Updates. But you do show up in their followers list, and anyone can open that from their profile. Unfollowing is just as quiet.
Will my followers see my wishes?
Only the wishes on your lists set to Everyone show up on their Home. Following doesn't show them anything from lists set to Anyone with the link or Only me. To change a list's setting, see "Who can see my wishlist?".
How do I see who follows me?
Tap the follower count under your name on your profile, or the following count next to it for the people you follow. A count of zero doesn't open. Every row has its own Follow button, and "Follows you" marks people who follow you back.
How do I unfollow someone?
Tap Following on their profile, or next to their name in your following list. It unfollows straight away, without asking first. You'll see "You're no longer following" with their name, and their wishes leave your Home. Tapped it by mistake? Tap Follow again.
Someone bothering you? See "How do I report a profile or a wish?".
Tips
Nobody emails you when someone you follow adds a wish, so check Home when their birthday or another occasion is coming up.
To find people you both know, open a friend's following list and follow them from there.
Want friends to follow you? Set the lists you want them to see to Everyone, then send them your profile link: see "How do I share my wishlist?".
Spotted something on Home you'd like to give? See "How do I reserve a gift?".