Flash drives, or thumb drives, are cheap and convenient, but because they are so easy to use and misuse, they are prone to corruption. The biggest way you can screw up your flash drive is to eject it improperly.
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Macs in particular don't come with much documentation, so you may not have the right directions either. There's a small delay in ejecting disks on a Mac that confuses many people. Macs also have a way of holding on to writable media like flash drives and thumb drives.
When you insert your flash drive into the USB port, does it have a little light that blinks on and off? If it does, that's good, because that light tells you when the computer is accessing the drive. Most drives have a blinky light, but if yours doesn't, consider buying a different one.
When you want to remove your flash drive, you first have to "dismount" the disk from the system. On a PC there's a little menu item in the lower right corner where you can choose "safely remove hardware" or something like that. On a Mac, you have several choices to remove the drive. The easiest and most common way is to drag the disk's icon to the trash.
(Note that when you do this, the trash icon turns into an "eject" icon - which is a line and a triangle pointing upward. In the old days people used to be afraid to drag their disks to the trash can for fear they would delete their files. So they changed the icon.)
Wait until the icon disappears from the desktop, but DON'T PULL IT OUT OF THE USB PORT YET. Look at the flash drive. Is the light blinking? If so, leave it in. When it stops blinking, you can pull it out.
Sometimes the computer refuses to let the flash drive eject. It will tell you that files on it are still in use. It can't eject as long as the computer is using the drive. The problem is that your applications sometimes use the drive, even after you are finished. So if you get this message, first make sure all docments are closed, and if that doesn't work, quit any applications you were using with the flashdrive. (Glance down at your dock - there will be a little black triangle under each icon with an open application.)
If your computer just won't let go of your thumb drive, even with all applications closed, you can try two other measures. Use option-command-escape to bring up the "force quit" window, and choose the Finder. You can't actually quit the Finder, but you can "restart" it, and that will cause the screen to blink and redraw. If all other applications are closed, you should be able to eject your flash drive after that.
On rare occasions, some process may still be locking up your flash drive. The last resort is to shut your computer down. When it's off, it's always safe to remove the usb flash drive or thumb drive.