Hi and welcome back Commander. If you scroll down the buy page on the main site you'll see a link to the Frontier store, or directly here
https://www.frontierstore.net
Log in to your account with the email you used originally (if you've forgotten the passwod then the usual reset link will be sent ).
Click on My Account and then "My Downloadable Products", you should see your original purchase there and a download button. This will start the install process. Just to be clear this method has no connection to Steam, you are dealing direct with Frontier.
If you've successfully logged in to your original account but for whatever reason it's not showing or you can't download it etc. then contact Customer Support, they are always very helpful in these situations. I'm not sure if you last played pre or post Horizons but if it was pre then even more has changed and you are missing out badly if you don't upgrade.
If you need any help with all the new stuff then head over to the newcomers forum where there are plenty of veterans and newer players happy to help. Fly safe!