What is the best way to promote my new adult Dating site?

[ABC]

There is two kind of marketing you can do on search engine to promote your website.

SEO - which gives you natural search engine rankings
PPC - Pay Per Click this will give you higher ranking but it won't be natural. it will show in the top of the Google result with light yellow background. Also you have to pay for every click or impression.
SMO - Social Media Marketing, Promote your website in social media platform like, Facebook, Twitter, LinkedIn, Google Plus again you have both paid and free option on this SN platforms.

Or if you have some budget allotted for marketing and promotion, hire an internet marketing agency.

God Bless All