First you should unmount any other exteral drives connected to your laptop in order to avoid mishaps. Simply plug them out.
Now that your external HDD is the only connected external drive you can start the installation from your LiveCD/USB. When you are asked for the preferred partition tabel configuration select the option to configure the partition table manually ("advanced" in newer verions "something else"). You can now change the device from your internal HDD (usually sda) to your external HDD sd"something" (easiest way to figure out what is what in this case ist to look for the capacity)
Now you have to create a partition table for your external harddrive. here create a partition for /(root), a swap partition (in case your ram runs out of memory this partition will be used to extend the hardware-RAM, you can skip this if you have above 16GB, they will barely fill up), a /home partition (this is where your personal data will be saved) and VERY IMPORTANT the location of the bootloader.
The location of the bootloader HAS TO BE on the external drive as well. If you install in on the internal HDD GRUB (the bootloader) wont recognize the OS installed on the external drive. Messing this up takes quite a time to repair. So check carefully at this point.
After that your Masterbootrecord is complete and you can proceed with the installation normally.
As mentioned, your bios boot priority finally has to be changed to look for the OS on the external drive first.