Yuyushiki will begin airing on Tokyo MX in April 2013.
As with most 4-koma anime adaptions, there isn't a deep underlying story to Yuyushiki. It simply tells the story of the everyday life of Yuzuko, Yukari and Yui, who are three members of their school's data processing club. They get together and talk about all sorts of things in adorable ways.
The official website for the show can be found here.
There isn't a special character page yet, but the website is likely to be updated soon with more information and character descriptions.
This short trailer comes from last year's Comiket. If it was eaten by YouTube, you should be able to find a replacement with this search query.