Pandora Music currently has no way to export your personal music preferences. There is an API, but it's currently not open to developers for use.
To get around these limitations, I created a website scraper to pull your liked (thumbed up) music into a JSON object that can be saved to you local filesystem.
If Pandora changes just the slightest thing about thier HTML class structure, this script will break. There are other similar scripts around that no longer work because of similar HTML structure changes.
I used Firefox and it worked well. Here's the URL you're looking for (you must be logged into Pandora).
https://www.pandora.com/profile/thumbs/{yourUsername}
You can also find this by clicking your profile icon in the upper right of your screen, then choose "My Profile", then "Thumbs Up" from the left hand menu navigation.
Your screen should look similar to this:
In Firefox, this is the wrench icon in your browser. It may not be a visible icon. If you're new to developer tools, you can start exploring them here.
Once opened, you're going to want the "Console" tab.
Copy the script in full and paste it into the console tab. Then click Run.
This will take awhile to run. You should see a counter in the console counting up as it adds the new records to the array.
You should see some text that states "Here is your collection of liked songs in JSON format". Right click the line below that and choose "Copy object". Paste the contents into a file and save it locally.
You now have a file that contains the name, artist, channel and pandora links to all your thumbed up content.
Have fun!