For most events, press badges are given to legitimate members of the press. In exchange for free admission - and maybe even access to areas that are unavailable to "normal" event guests - the event organizers expect to see photos and documentary coverage of the event in a legitimate publication. A personal blog generally isn't enough to warrant a press badge, and it's generally frowned upon to use your camera to pretend that you're a member of the "real" media.
The usual answer to "How can I get a press badge?" is "Your editor will secure one for you."
For smaller conventions and events, you can probably contact the event organizers directly, with the expectation that you will supply them a certain number of finished images in exchange for your press badge. This wouldn't fly with something big like Dragon*Con or SDCC, where they have plenty of coverage by well-known media outlets, but it might work with small local cons and expos, if you have a portfolio of event coverage to back it up.
I wouldn't be opposed to paying for a special photographer badge that included an ad for my business in the program and/or website.
cliffs: don't expect to get in free just because you're carrying a DSLR