I'm taking a guess that everyone will have their own methods. Some that are tried, tested and failed and some methods that work.
If you are on your own, I suspect your task ahead is going to be slightly more tedious than if you there is at least a few within your social group who are willing to help out.
Some suggestions:
Use google, to locate equivalent parenting sites, if some of those sites do not have their own forum, think about contacting the webmaster/owner of the site and attempt to at least exchange links.
If there are other parenting forums, then you may want to join them and put your own forum link into your sig, without informing anyone you are the owner of the site you have in your sig. (this also applies to any forum/site you are a member of)
Another suggestion could be to contact good parenting organisations and let them know you have a responsible discussion forum etc. Perhaps they may pass this onto their own site visitors/members.
Use IBP (internet business promoter) to submit your site to a lot of search engines. It can be purchased or downloaded as a torrent for free.
Another idea is to register on a site that has a groups facility such as Yahoo for example. Find the relevant groups, join them, spam them in the nicest possible way. Use a different email (again google is your friend). Allow yourself to accept individual emails, then harvest all the email addresses from the incoming email, download emails addys, upload to a new email address and then send out a polite email advertising your site to all the email addy's you have harvested.
Then there is also joining the social groups like facebook, myspace, etc, and advertise you site. Programs such as Easyadder can be your friend to harvest friends on myspace. Join relevant groups on facebook and work on it.
Submit your site to MSN, Yahoo, Google and Dmoz and any others that you can do direct.
Create a blogger site, and throw your site links into a few of your own blogs, and then digg 'em.
Another one is to put your site name into mp3 comments, and go filesharing, (not sure as to how this pans out, as I've never tried this one, but a friend of a friend who knows a friend who happens to go out clubbing with a mate of mine has tried it.)
Anyway, as Alexander from meerkats.com would say 'simples'