Best free ways to promote the game would likely be
A) place it on the chrome webstore
B) make some youtube videos of the gamepaly
C) If you feel like going the extra mile blog about it. Making regular entries on game updates and upcomming features etc.
A lot of small game companies promote their games through blogging. Most of the time the posts aren't about the game, but are technical / design posts aimed at other game developers, or even just random stuff. See altdevblogaday - many of the posters there are startup founders / members. (In fact the 5th post is Promoting your indie game company with a podcast)
You can give referral bonuses to players that sign up new players. Get the players to do the advertising
Hey turch, thanks for referencing the podcast post from our blog
I think the biggest tip I can give you is to find communities relevant to your game and be straightforward with them. Say that you've been working on the game for a year, think it's something they would like, and ask them to try it. These communities can be on Reddit, forums, or otherwise. Use social media (Facebook, Twitter) not just to promote your game but to engage your fans. You've got to do things like in-game contests, giveaways, and cool pictures/videos to make the social content something people actually enjoy. The goal here is not to spam everyone about how great your game is, but actually create a community of passionate fans around your game. From there, you're off to the races
I work for Betable, a game monetization platform. I also write about startups, gaming, and marketing.