The best way to monetize a free game is to charge for it. The quality of freeware on the internet has risen tremendously in the past few years, and it's gotten harder to make money off of free games. If you want to make money, I suggest you spend some time making a commercial game.
Putting ads up on your game's website is probably the best bet for making money off it.
Ads are worthless nowadays. Unless you have a website that is getting thousands of hits a day, you probably won't even get accepted into an ad service. There's always Google Ads, but those make even less, and you probably wouldn't even make enough to reach t he minimum payout amount.