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I'm looking for an RP fleet that is accepting low level players ( I'm Lt.7) and will accept the fact I have some obligations to a guild in guild wars 2. I've played quite a few of the free to play mmos, and this is the first that has kept my interest. (as I said though, I do have some obligations to a GW2 guild.)

How does the RPing work in STO? I am interested in RPing but how do you guys do this?

Think of it as acting (improvising in this case) for amateurs. In this case: gamers.
On a simple level, you start by creating your avatar.
You create a story (doesn't matter if its sparse or complicated), and you work around your characters story with others. (That's how a Stanislavsky type approach works).
For games like STO and/or Discovery mod for Freelancer, you improvise the words and actions of your characters based on the events or actions of your fleet mates.
Another way to role-play is on the forums. For example, your leader creates a post concerning a skirmish that happened in say Klingon territory, say Kerrat, and you improvise YOUR experience in reference to your leader's (or other member's) experiences.
Since STO doesn't allow random attacks by somebody in any system, usually you role-play with friends or enemies on events that have happened or are going to happen.
Where as with Discovery mod for Freelancer, ANY type of event can occur at any given time, anywhere, so there you have a chance to improvise IN THE MOMENT; in-character.
Since random events can't happen (usually) in STO, you have more time to add details to your characters personality/story, and then use those details as a basis for how your character will act during various instances.

I am familiar with RPing on forum and such,.. I am just asking how you you technically RP ingame? Isn't it difficult to type and move about.. using emotions etc live?

Well, as I said, considering the fact that STO doesn't allow random events, like Discovery mod for Freelancer, its much easier to type and converse with someone.
Of course, if you don't have qualms about using a microphone, that's an infinitely better way of doing it. But considering that amateurs - that is, if you are NOT an actor in real life - are usually embarrassed by their own voice, and many a time have difficulty with improvisation, when trying to act out scenes, they usually prefer to type. And of course in a game, where you usually type, it gives gamers more time to think of what they want to write in the long run.

P.S. it gets easier with time. Especially in STO. And since there are gamers in STO who have become quite good at improvising story-lines you'll have some good practice!

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The major stumbling block I've run into with using voice is the player's voice not matching up with the character. You are RP-ing with a female Vulcan, whose player speaks with a deep male New Jersey accent... it kinda throws off immersion. Not to mention once you hear a player's voice, that's what you hear in your head for every character they play from then on, regardless of voice chat or not.

I have two more to add to your list:

United Sector Taskforce
The Storytellers

I'm a member of UST. Good group of people. We're at the brink of a tier 4 Starbase and have a tier 2 Embassy.

oh yes definitely LOL
Well obviously you can just do voice interactions with players whose avatars are the same gender