If the trial version is the same edition as the full version you purchased you can easily upgrade by entering the new license information.

Example:

You are using the Vivid Content Basic Trial and you want to upgrade to the full version of the Vivid Content Basic edition.

1. Purchase a License for Vivid Content Basic from the Vivid Tools Web Store
2. The Vivid Tools License Management Server will provide you with a license file called license.lic
3. Login to Joomla administration. Select Components -> Vivid Content -> Home from the main Joomla administration menu
4. Click the License Information Panel and copy your license into the text box.
5. Click the Update License button to save the new license information