How can I find out how people discover my website and keep them coming back?

Google Analytics.

I use google analytics too along with gostats as I like to compare the results.

I think through google analytics we can know the website traffic and the users but to make people coming back to their website, google analytics won't help you out..

Then you're not using it right. You can use GA to determine your most successful landing pages, and the origins of at least some of your traffic.