An open beta or an initial limited access for 100 users, or something like that? If it's a good game, it'll grow organically from there. Encourage people to share their experiences via Facebook and Twitter.

Promoting a game especially when it's brand new, is really hard.
You need to have a lot of funds and/or a good team of marketing experts, community managers etc. to help you with that cause.

If the game is great, your word of mouth can do wonders because after all we nowadays rarely play alone ;)

Some areas i'd surely check out is:
YouTube video right before a gaming video.
This works both ways, you can do your branding and raise awareness even by people skipping your video (and you paying nothing for it) or in the other hand, pay 1-2 cents and have someone view your video and see if the game works for them. HIGHLY suggest this.

Ask for some "beta" testers on gaming forums.
if the game is new, many people will come check it out as they love being first in a great game and learn the ropes early.

Create an inforgraphic.
about the gaming industry or your game genre. This will help with links, awareness and seo! ;)

Try to create a community.
And this is the most important of all. Check out clash of clans forums or even their fan page. Also check league of legends fan page too. The second they upload something, there are thousands of comments. So the friends of their commenters see that their peer has commented on a game and they check it out.

Buy some banners on targeted websites.
For example if your game is a moba game, i'd surely go to the league of legends subreddit on reddit and buy ads there.

There's an infinite amount of things you can do to promote a game but it all comes down to time you have and available resources / business model for the game.

I'm new here and trying to check clarity out and since I LOVE games and game promotion, heres my free call link so you can call me free of charge and we can talk more about it, hope I can help you a bit with more and more precise pointers according to the game you want to promote.

My link is: https://clarity.fm/moneytized/moneytized
Cheers,
Angel