First, you must determine whether or not your computer will be able to boot from a USB drive. You check this from your computers BIOS options (usually in Advanced>First Boot Drive).
Then, you must determine how your curretnly Linux installation recognizes the drive (for example, sda1, etc.) Once you have determined these things, then you can install the new Linux distro and add it to your bootloader configuration pointing to the correct drive to boot.
Hope this helps