Like others have said, asking friends and family to check out your site is a great place to start.
Its also a good idea to reach out to people on Facebook, twitter, etc. Don't spam people though. The idea is you want quality members that will participate in discussions, not someone to click a link and close it. Think of it as making friends, not trying to trick people into visiting your site.
Typically, when you try to find "get members quick" schemes, they end up not working well. Its important that you get some good dedicated members, especially when you're first starting. If you put in a great deal of effort, people will realize that. For instance, if you are a great programmer/coder, and you come on the PhpBB site and start helping people with their problems, they are likely to check out whatever site you have in your signature. You can join any type of forum related to a skill you have and help people. Not only are you helping people, but you're also advertising. Furthermore, when people randomly find your posts through Google, they'll see how helpful you were, and be more likely to check out your signature.
YouTube is also a great place to advertise. Its very easy to contact someone that makes videos with a few thousand views and have them give you a shout out in their next video. Of course, you should offer them something in return, like a link to their videos on your site. You can also post in video comments, but again, spamming really doesn't help you. Only post if you're actually contributing.
Its a good idea to market your site 1 on 1 with people, or to small groups. Its not something that will pay the bills, but its something that will get you dedicated members. Once you have dedicated members coming on the forum everyday and posting around, you'll be able to start entertaining less dedicated members.