If you have made a website and are not waiting for the traffic to come, then there are few things you need to know. The traffic will take a while if you want it to come naturally without spending money on traffic or advertising. And that too is promised only if the website has high quality content and addresses a real need of the visitors which is not being addressed by other websites in the way you have attempted to do.
The other way of building your website as a brand is to buy traffic which can come in the form of advertising. That is a quick results method. So you need to first ask yourself this questions: do you want the traffic to come naturally, which might take more than a few months or you want it right now?
First you can try to engage in forums related to your niche and start participating there with a link to your website with a well written copy as signature. However, this will take some time and you will need to persist to see results this way. Once you start participating in high traffic forums related to your website topic with high quality posts, people will slowly start taking you as an authority and you will see your website growing as authority and as a brand.
When it comes to using Facebook as a tool to build your website brand, you can attract high targeted traffic based on the demographics and likes you choose for your ads. Try to split test your ads for best results. Run two simultaneous ads with two different pictures and see how they perform. Discard the low performing ad and keep the high performing ad. Also try to tweak the text of the ads and split test to see which text performs better. Keep repeating the cycle and you will be decreasing your Facebook advertising cost quite significantly in the long run. However, do not let the low performing ads run for long because you might make your Facebook advertising budget shoot into the sky.
In short if you are not willing to spend your money on building your website brand, then you will need to explore other ways like forum participation, social media and other such methods, which are definitely going to take more time for results.