My side project is a course about Vue.js [0]. I advertise it by putting a backlink on all my free content, including blog articles/free book I wrote about Vue testing [1] and videos I upload on Vimeo, and via my Twitter.

I also joined some discord channels, and help out people with coding problems. If something in my book/course is similar, I drop a link to that (after resolving their problem).

[0] https://vuejs-course.com [1] https://lmiller1990.github.io/vue-testing-handbook/

The best way to advertise is providing some useful, valuable content for free. If people like it, they might also buy your paid content.