There are tons of different ways to market your side project and what works for someone else may not work for you, of course.

I think it really just comes down to where your potential customers may be hanging out / searching. For my side project, I've had decent success responding to posts/questions on sites like Quora, where someone is looking for exactly what you offer. It's free too (besides for your time!).

The book Traction (https://www.amazon.com/Traction-Startup-Achieve-Explosive-Cu...) gives a pretty solid overview of different marketing methods/strategies.