Blogging as your character can be as simple as writing a blog for yourself (but a lot more interesting) The idea behind this is pretty straight forward - you're writing a journal as if it were kept by or about your character.
The journal doesn't actually exist in character so it can't be found and used against you... (although you can make entries actually exist in game by making note of it at the very top, first sentence, of your post) it's just a way to share your character's mind set, personal thoughts, and such with storytellers & other players while providing an interesting way for your to explore their mentality in an entertaining to read fashion.
It should be made clear this is NOT where roleplay takes place. Forums and chatrooms is where your in character interactions occur... journaling is a way to reflect on roleplay that has already occurred or to write about events and times when your character is completely alone and away from the rest of the other characters.
There are several styles which I have seen that work well, here are two I've enjoyed but really there is no wrong way to journal for your character:
1. The diary - written by the player as if they were their own character keeping a diary to reflect on their inner most thoughts and feelings.
2. The movie - written by the player as if telling the story of their character's life to another person or an audience. It reads rather like a movie is watched with descriptive bits of text often describing the character's body and actions as much as their thoughts and words.
If you're still uncertain about how to blog as your character, talk to the storytellers or game organizers and we'll be glad to help.