There are several paths:
- Paid Advertising. This is thought of as a requirement in the industry currently, as the usual word of mouth and viral spread techniques that might otherwise boost awareness/traffic/signups run up against issues of privacy and fear of disclosing the use of an online dating site to a wider circle of friends. People may feel less reluctant to admit the use of dating sites these days, but it's still not something they heavily promote/advocate on their own. Another form of advertising, the affiliate sale model, pays third parties to convince prospects to sign up for a site.
- SEO. By identifying revenue-generating niches, and performing keyword optimization techniques on one's site, it is possible to rank highly in medium to low-competition niches, and thus increase traffic flow for people searching within a particular niche.
- PR/Media relations. If a company can convey a newsworthy story, to the right outlet, when they aren't busy covering other breaking news, it's possible to receive online press coverage fairly easily. Once more established on blogs/news sites, these press hits can show social proof to get access to print and cable news channels. Performed wisely, with recurring news every quarter or two, a site can build traffic via appearances in the news.
- Fake user databases. This is a more popular tactic than you would think, or like. Sites can purchase lists of "members", along with pictures and profile text, for a very small investment, then "seed" their membership in a way that makes it appear that they have a strong user pool in any major (or even small) city. This gives any real users a greater incentive to join up. As this effect snowballs, the site can slowly delete/remove the fake users, as enough users come online in a given area to achieve "real critical mass".
- Shared user databases. This innovation allows you to license another site's user database for your own site. The users themselves are instantly "members" of the new site, which gives them even more ways to be found/matched/selected by compatible people. In theory, this means getting to critical mass immediately, in exchange for a licensing fee. Since this is similar to a lot of software/content licensing agreements, it appears attractive. Unfortunately, there is a large amount of overlap between #4 and #5 – so you may wind up sharing a database that is largely fake accounts. As Yosemite Sam might say "Two Nothin's is Nothin!" It's also possible to license accounts that are 100% real, verifiable, and simply inactive. Three Nothin's?
- Innovation. This one is really really hard to get right, and sustain over the long haul. It may take much longer to grow to a decent size, but services like OKCupid initially pursued this route – since the site was so different from the big online matchmaking catalog sites, it became a word of mouth alternative. Eventually, though, OKC also invested in regular large marketing spend to attract new users, as their "known brand" elements had become so established and familiar, that making significant/drastic changes had a greater chance of upsetting existing users than attracting new ones.
Basically, there is almost no difference in HOW free sites attract new users. The main difference is the subscription price (free), and the perceived value proposition associated with it. This also means that there is some form of market targeting/segmentation going on between free and paid sites: free sites cater to everyone in theory, whereas people of certain income levels/philosophies are essentially blocked or self-selected out of paid sites.
Perhaps the extent of issues/complaints involving paid sites acts as an additional incentive: it's very hard to prove the old saw "you get what you pay for" when it comes to online dating… Mostly because people confuse what most dating sites are offering: access to their database, and nothing more. Free sites, then, only have to provide the smallest perceived value to become "value positive" in the mind of the member – something as small as a single email reply in a month. The same situation on match.com or eharmony.com would be seen pretty universally as a waste of the membership fee.