If you have registered the keys on Blizzard website, simply follow these steps:
1. Enter Blizzard website :
https://www.blizzard.com/en-us/2. Enter your Blizzard account associated with the Diablo II key
3. Click on your name and the press "Account Settings"
4. Click on Games & Subscriptions at the menu to the left.
5. Scroll down to "Classic Games"
6. Click on "Download Game Client" on the same row related to Diablo II.
7. Install the game using the key you saw in step 6.
8. Have fun.