I have a 180 GB SSD on which Windows 10 is installed. And I added a secondary 500 GB HDD caddy in DVD-ROM in which I have some data, movies, songs, pictures etc.
Now, I want to install Ubuntu on that secondary HDD. I mean one partition is Windows and on another one partition, I want to install Ubuntu.
How to do it?
I did initial steps but I'm stuck at the point when I have to choose the drive on which I want to install Ubuntu.
Because you have a specific scenario, you will need to choose "Something else" in the installer, and assign partitions and mount points yourself. A good general outline of how this works is already provided here on Askubuntu. I am providing some remarks specific to your case.
1 Partitioning
You will need to create a separate partition on your 500 GB that can contain your Ubuntu system. If you do not plan to store many user data only accessible to Ubuntu, then 20 GB is enough. You may then replace your data folders by symbolic links pointing to other partitions.
2 Partition assignment
In the most simple setup, you only need a single system partition. Ubuntu since 17.10 does not anymore set up a separate swap partition, and uses a swapfile instead. Click the partition where Ubuntu needs to be installed. Click the "Change" button to edit the partition and indicate for "Use as": ext4, check the box to format the partition and under "Mount point", indicate / (root). There are several screenshot in the linked answer.
3 Device for boot loader installation
The installer should automatically have selected your Windows SSD drive to install the bootloa.der. If not, change the setting to that drive. The system will then continue boot from that drive. Upon booting, the bootloader will load Grub, which will present a menu where you can choose to boot into Windows or into Ubuntu.
