After I started up my game for the first time and after installing it I'm being prompted to insert the CD.
How do I resolve this issue.
Thank you in advance for the help.

This was a bug with older versions of the GOG standalone (offline) installer that was supposed to have been fixed. If you originally downloaded the offline setup files for the game a while ago, try re-downloading again or use GOG Galaxy to install.

If that doesn't fix the issue, then try manually editing the following registry key and point it to the game's install folder:
HKey_Local_Machine\SOFTWARE\Wow6432Node\Blizzard Entertainment\Archives\DiabloCD

Note: if you're still running a 32-bit version of Windows, the path would be:
HKey_Local_Machine\SOFTWARE\Blizzard Entertainment\Archives\DiabloCD

In theory, the GOG installer should set that key properly, but anti-virus software or other security settings may be preventing it from doing so.

GOG employed a couple of different hacks for making the game not look for the game data on the CD depending on what version you run. Some of them aren't supper reliable.

Besides Ryan333's suggestion you can also use DevilutionX to run the game. This has some additional benefits like smooth mouse moments and widescreen support.
https://github.com/diasurgical/devilutionX/releases
(as the maintainer I am super biased)