Depending on your machines specs, (BIOS) it may not be capable of booting from a USB device. If that's the case then you are snookered really.
If it is able to boot from the external drive, Then...
1) Start your machine, navigate to your external hdd
2) Create a new partition with the required space on the drive. (this will ensure that your data on the previous partition will be retained)
3) Install the new os
4) If all works well (and you need to check this first)
5) You should be able to boot from either your internal drive(s) or your external.
Need mobo and PC specs to confirm.