There's no one way. Here's a recipe you can use:
Make a proper app post here on StackApps.
See How to list your application/library/wrapper/script here.Look for posts on Meta Stack Overflow (MSO) and/or on Meta Stack Exchange (MSE) where your app might make part of a good answer.
If you find such posts, make proper answer(s) to them -- linking both to the app post you made in step 1 and directly to where they can install the app.
Be sure your answers meet all the regular criteria of a proper answer and avoid "spammy" behavior.If you can't find such posts, you can create a self-answered questiona self-answered question on MSO and/or MSE -- provided that such question and answer are appropriate to the site.
If you have a blog, Facebook, Twitter etc. You can promote your app there, too.
PS: You can always pay me large sums of cash for advertising purposes. Results are not guaranteed. YMMV. (^_^)