For my site, Scribophile, it was a classic chicken-and-egg problem. You post your writing for critique, but must earn points by critiquing the writing of others first. This is what I did when I launched:
-Nobody will join a site if it looks like a ghost town, and sites always begin as ghost towns. So I had a lot of my friends create several accounts each and just futz around to give prospective members the illusion that the site was older and more active than it really was. I personally critiqued people's writing under several pseudonyms, and even though I don't write much myself, I sat down and wrote some stinkers just to post on the site to make it appear active.
-As I mentioned, you must critique writing to earn points, but you can't earn points if there's no writing on the site! So the first few hundred members got the ability to post their writing for free, without spending points. This seeded the site with some content--low quality content, but content nonetheless.
-I had a paid account option in place from the start (freemium model), but at first everyone who signed up got a free upgrade without them knowing it. That means they got to use the site to its full potential, and thus seed it more effectively, while I was growing the user base. They told their friends about this great new site with all these features... and once I felt that things were rolling along smoothly, I flipped the switch for new signups to start with a free account versus a downgraded account, so I could start getting paid. (I grandfathered in everyone who had signed up up to that point.)
-I spent a lot of time personally canvassing writer's blogs and offering them a free upgraded account if they were interested in joining and participating. Never mind that anyone who joined was automatically upgraded like I mentioned earlier! Writers write a lot (naturally) so finding blogs belonging to writers was pretty easy.
-I set up a few free writing contest with big cash prizes to launch the site. The catch was that instead of submitting your piece via email, you had to post it to the site using the points you earned from critiquing. So I basically "bought" early activity in that sense--both more writing to seed the site, and critiques, which is the most important thing.
-Along with relevant blogs, I also posted in forums telling people about my site. Turns out most forums aren't too interested in having someone sign up just to advertise their new venture and then disappear; so instead of advertising that I had launched Scribophile, I advertised the free writing contests I mentioned above. Seeing "announcing a free contest with cash prizes" is much more tempting than "hey guyz, come see the new web site I just made, pretty please use it!"
That's all I can think of right now off the top of my head. 3 years later and Scribophile is paying my bills and still growing strong.
Obviously things will vary greatly from case to case, but the takeaway is that it takes a lot of hard legwork, persistence, and maybe even cash to seed a site with users. Launching isn't the finish line, it's the starting line.