As suggested above, there are many ways.
One is to follow Mint's web pages or www.pendrivelinux.com
for easy ways. Those installs are pretty safe. They use either the native app or a third party app to convert a live cd/dvd to a usb.
Second is a way to just take a special iso file and use dd command to install it to your usb. BE CAREFUL. dd is a command that has no opps key.
Third is a way common to most modern distros. A usb is used like an internal scsi drive. In fact an IDE drive is treated like a scsi drive as well as a sata. All appear to linux as a real hard drive. That means most installers just ask you where you want to install the OS. Be careful here too. RTFQ comes into play. Read the F question. If you hit OK, OK, OK you will be back here.