The story telling style is what you will see most on Role playing Forums due to the nature of Forums and people replying. It gives Rpers more to work with and is easier for more people to join at will then a Tag based Rp or to catch up if they have been offline a while.
The basic use of the Story telling style is just that, to tell the story, unlike tag based story telling tend to be ALOT of heavy reading, and alot of discription, however this allows for ALOT more story to be read at once and allows for quicker plot progression all at once.

Unlike Tag based pretty much everything comes under the one element of story writing, everything can litterly be done in one flowing movement so to speak, for example when your character speaks he speaks with " marks either side to show they are speaking. generally with speech there will be an "introduction" to them speaking for example Sirus turned to his freind muttering a few words "you know..i really dislike this guy" Just by that one sentence you have been able to Say who it is, who hes talking to, how hes saying his words, and what hes said. Thats the flowing movement.

Actions in story telling style will always be discriptive, unlike tag based where using a * action is quick and Generalised story telling you need to be alittle more precise, the best way to example this would be to do a comparison.

tag based:-
Sirus: *unsteaths his Scimitar*

Story telling:-
Sirus quickly unsheathed his Scimitar from the scabbard on his back.

That was a very basic example but gets the point accross.

Because this will be written like abook, you get a little more freedom to type then you do with Tag based. But however, compared to The easier to follow tag based you need to remeber that people will need to be able to read what you have put and understand what you mean, and that it is relevant to the plot.

If your doing a scene with someone else and your character is interacting with them then you need to leave "open ends". Open ends basically give the person your wanting to respond a place to retourt with their own character. An example of this would be As they waited Sirus walked over to Aira arms open to hug her
now Sirus isnt hugging her yet which gives me the option to either let Sirus hug Aira, or prehaps have Aira knock him away and not want the hug. Most of the time you want to keep things open for other rpers, as rpers generally do not like having their characters forced into actions.
Now you can have "closed ends" as long as its something that can be left open later. again using the hug example Sirus walks over putting his arms around Aira hugging her
Sirus is now hugging Aira, now i can do something with this, but im restricted to the action being revolved around the hug. Examples of actions would be Aira squirms uncomfortably as shes hugged or Aira quickly shoves Sirus off stepping back from the hug
This means you have retorted but now you have to wait for the other to respond to the reaction of the hug, so use closed ends only if you know that the person you are doing it to has space to work.

Whilst doing story book rps you have to remeber to try and set up the people you are rping with when it comes to interaction. An example of this can be seen in the "strange new worlds post". I wrote Saying that the Emerald had hailed the Acadia and Voncloud started to talk. This gave Curst the notice that he was being contacted and that the next action was his.

I wont put an example Rp as this site is littered with them, so happy hunting.
Any questions or additions feel free.