I would think with humans expanding their knowledge and exploring the galaxy, posting pictures of their lunch, or mirror pics of their new bathing suit so everyone can "LIKE" it probably isn't really of much interest when you can be going where no man has gone before!
I'm sure there are news wires that send information out to relay stations so everyone can hear updates about political events and such. Jake Sisko was a reporter/writer for the Federation! He wrote and sent out lots of information. And as stated, I'm sure that technology has allowed everyone to be able to access any information they might need from a Starship or Starbase. And I'm sure there are terminals the same way on earth. I don't think there would a need for the internet the same way we use it today. I think it would be far more integrated into peoples lives without even realizing that they way they send and receive information was based of the internet as we use it today.