The application will continue to show the 30 day trial until it expires. After it will display the subscription you purchased.
You can see your purchased subscription in your management portal (AMP).
https://help.sketchup.com/en/account-management-portal
If you are the admin for the subscription (most single purchases will be both Admin and user), you will see the subscription you purchased.
In the Members area of the AMP, you will be able to see the subscription seats that have been assigned and you will have the ability to provision un-assigned seats to users on your team.