Q: Updating Final Cut Pro 10.0.6 to work under Yosemite - MacBook Air

You need to log in to the App Store with the same Apple ID used to buy it. Look for Final Cut Pro in the Updates section and click Update.

The current version is 10.2.2.

NOTE: The application has changed quite bit since 10.0.6. Especially the transition from 10.0.9 to 10.1 changed the way it manages media, introducing the concept of library. You should read up on this change before you proceed. Libraries now contain events, and events contain clips and projects.

This is a big change for the better, but it is a different mindset.

Before you proceed, read about the library model, for example

here: http://www.fcpxbook.com/

and here: Update and work with Final Cut Pro X libraries FAQ - Apple Support

Don't worry. It is a great improvement over the old scheme. Totally worth it.

Once you've downloaded the app, start here

http://www.fcpxbook.com/updates/101/101libraries.html

to learn how to work with the newer, significantly different, verisons.