dual boot - Installing Ubuntu without sharing a Windows partition or replacing Windows

I am quite new to Linux and the concept of using dual operating systems. I am aware that the Ubuntu installer gives the options of sharing the Windows partition or replacing Windows. I would like to do neither of these.

I have a notebook with and SSD and two HDDs. The SSD (c:) houses Windows OS and the first HDD (e:) is used for Windows file storage. I would like to retain both of these drives as is and install Ubuntu on the second HDD (potentially f:), which is currently blank and unformatted (brand new).

I would also like to have the OS choice option on boot up that would be given if Ubuntu were installed sharing the Windows partition. Is this possible?

If this is doable, how do I go about doing it?

I'm assuming then that you have the wubi.exe installer because of how this is phrased.
Using the wubi.exe installer Ubuntu will be installed as an application on windows. It will appear like a dual booting system (even has an Ubuntu option in your bootloader) but it won't be on its own partition or anything, it will simply be stored in the Windows directory you installed it to. What you want is an actual installation on its own drive.

In order install Ubuntu on its own drive you will need an ubuntu iso file. Those are from the Ubuntu downloads page, pick version 12.04 or 13.10, doesn't matter which. You will need pendrive Linux or similar program to create a bootable usb key or CD out of the iso file. Make sure to follow the steps very carefully when selecting the drive because pen drive Linux can break your system. Once you have the bootable USB or CD, start your pc with it plugged in and boot off the USB.

How to boot from the USB depends on your system; some will do so automatically, some will require you manually enter the boot menu and select it. Once in, you will pick your language and some other settings. Eventually you will get to a menu where you can pick your installation type. You will probably want to pick the "Something Else" option, this will allow you to select the empty external drive as the install location. This guide should help you out if pictures make things clearer.

After Ubuntu is installed, you may need to change some BIOS entries. Specifically, if Ubuntu is not a bootable option after installing it you will need to make sure your settings allow booting from external HDDs.

NOTE: I did some searching around and found this question that sounds very similar to yours. The answer by izx is very detailed and explains how to install Windows XP and Ubuntu onto two separate drives and still get both to appear in the boot menu. If his answer works for you don't forget to thumb him up and give him credit.