How do I get rid of the colored rotating circle on my MacBook Air?

It means that something is keeping your Mac busy. If it persists for a long time it's often because a program has not fully closed.

Try this - press the Option-Command-Escape keys at the same time. A window will open up listing the programs that are currently running. If any of the say "Not Responding," select that program and then click the Force Quit button. That will close the program and probably eliminate the beachball.

ALTHOUGH ... if this is happening during a software update (update/upgrade of macOS or a security update) you should not Force Quit it. Let us know and folks here will help you figure out what to do.