How do I properly eject a flash drive?

Right click on it, and select Eject.

You can also drag it to the Trash. When you do so, you'll see that the Trash icon changes to an Eject icon (same symbol that's on an Eject key).

By doing that the drive will be dismounted, and its icon will disappear from the desktop; once that's done you can safely unplug it.

The reason to use an Eject command or drag it to the Trash is to make sure the drive has been dismounted before disconnecting it. The act of dismounting it ensures that the OS has 'let go' of it. The risk in not dismounting it before disconnecting it is that if you just abruptly disconnect it, you may interrupt a write operation to the drive - and doing that creates a good chance of bollixing the directory on the drive.

Adding to the other 2 posts there is also a keyboard shortcut that will work when the item is selected:

Regards,

Colin R.