To share your wishlist, open the share menu, copy the link, and send it however you like: message, email, whatever app you use. Whoever gets it can open your list without creating an account.
Steps
Open your wishlist and choose Share.
Copy the link, or use one of the share options to send it directly.
Send it to friends and family by chat, email, or a social app.
They open the link and see your list: its name, description, and all your wishes. They can Reserve a gift so others know it's taken.
Before you share
A Public or Anyone with the link wishlist opens for anyone who has the link, with no sign-in. Reserving may need an account, depending on your settings. See "How do I make sure my friends can reserve a gift?".
Sharing a link lets people view, not edit. To let someone help manage your list, invite them by email and give them an access level. See "How do I invite another person to edit my wishlist?".
A plain link won't open an Invite only wishlist. For those you invite specific people by email. See "How to share a private wishlist".
By default you won't see which gifts have been reserved, so sharing your list doesn't spoil what you'll get. See "Can I hide reserved gifts from myself?".
Keep personal details off a shared list. There's no address field, and anyone with the link can view it, so sort out delivery privately rather than posting where you live. See "How to safely share delivery details".