If I stick a Sandisk Cruzer USB drive into my MacBook Air, and then encrypt it (via Finder), will my MacBook Air be able to use it seamlessly? Or will I be asked for a password every time I try to read or write to the USB drive?
You will be asked for a password each time you mount it (plug it in) or if you restart your computer.
Also note that you drag files to and from the drive the default behavior is to copy the items, not move them. If you want to actually move the files, hold down the Command key as you drag them and release them.
This is the window you will get when you attempt to mount an encrypted drive. You can choose to store the password in Keychain (a program that stores application passwords on your Mac, encrypted and tied to your Mac password), in which case the drive will be mounted normally without a prompt once you plug it in. Make sure you record the password somewhere though, in case you ever lose access to Keychain.
This is the window you will get when you attempt to mount an encrypted drive. You can choose to store the password in Keychain (a program that stores application passwords on your Mac, encrypted and tied to your Mac password), in which case the drive will be mounted normally without a prompt once you plug it in. Make sure you record the password somewhere though, in case you ever lose access to Keychain.
Right-click on it in the sidebar, it should say ‘Encrypt “[drive]”’. If it doesn’t appear there then the format is probably not supported (i.e. needs to be reformatted with Disk Utility).