I've had it since Dec. 29th.
I am just starting to find out about SEO and I linked to my blog in some forums, but it is still not showing up.
Since the blog is new, and you said you are new to SEO, here is how you check to see if your domain is indexed by google. Go to google and search the following:
site:yourdomain.com
(replace yourdomain.com with you actual domain.. ie- blackhatworld.com)
If it shows you results, your site is indexed. If it says your search did not match any documents, your site is NOT indexed. (means, google doesn't know it exists yet) To get indexed, you need some links pointing to your site, and then it can take some time.. it can be as short as a few hours, or as long as 7 days... The easiest way to get a good link pointing to your site, is create an account on jumptags.com (it's free, it's a social bookmarking site) and bookmark your site there.
One more important thing - because you said it's a new blog. Did you install WordPress? Did you install it using fantastico? If so, the DEFAULT setting is to NOT allow your posts to be indexed by search engines. (well.. this might have changed since 2.9 came out a short while ago)
Go to your privacy settings and change it. (Settings, Privacy, change it there) If it was set to "I would like to block search engines but allow normal visitors".. that's your problem right there.
Hope that helps!