To sign up and book an experience on playplanet, one should first go to the website letsplayplanet.com and click "Sign up/Login" to create an account using Facebook or email. After confirming the registration through email, you can browse and reserve local experiences created by locals. You can then book and pay for your reservation through options like PayPal, credit card, or bank transfer depending on your location. Once paid, you will receive a ticket and be able to add the experience to your calendar.