In a number of ways. The most basic thing is: You have to install Ubuntu on the new drive.
How you do this will depend on how you want to choose which OS boots when the system is turned on. If you will choose it in the BIOS, by selecting which hard drive should start the system, you disconnect the windows drive, connect the new one, install Ubuntu, and then reconnect the Windows drive. You now use the BIOS to choose which drive will start by default, and interrupt the boot sequence when you want to boot the other one.
Alternatively, you can allow the Ubuntu install, or a third-party boot manager, to build a boot menu. In this case, the system will always start the boot from (whichever disk the boot manager is on) and then offer you a choice of which OS to continue booting into.
We can provide more details if you choose which way you want to go. I, personally, use the BIOS method, but it is not popular.