If you were upgrading an existing trial team, there's no activation needed - you can head to https://app.getpostman.com/dashboard/teams to verify that you're on the paid plan.
For new teams, if you had selected the "admin role" during the payment process and were signed in, you'll need to sign in or sign up with the email you provided. Your account will automatically be linked to your purchase. If you were not signed in while making the purchase, check your email for an activation link.
If you selected the "billing role" during payment, an activation email would have been sent to the admin user you specified. If the user reports that they haven't received the email, you could direct the user to check their spam folder.