Follow these quick steps to use Reddit on your Apple Watch:-
1. Go to the App Store on your iPhone and search for the app “Nano for Reddit” or click on this link to install the app:
This app is for free but a few features might be a Pro feature which need to be paid for.
2. Open the app on your iPhone and login with your Reddit account in the app.
3. Make sure to have the app on the Apple Watch as well.
4. After the app is installed on the Apple Watch, you can use Reddit on your wrist.
You can now view your posts, upvote, downvote, comment, save posts, view subreddits, view favourites(paid feature), view your inbox and see your profile.
Have a glance at some screenshots of this App running on the Apple Watch:
Source: App Store