IMHO I believe it a mistake to think that RP needs to be an elaborate story, I feel it can be just as much a simple setup of responding with another to a particular environment. Much as Stray has presented.
The next step or tier in my mind is where one has created a personal space of play. Owning a room so to say, and creating it as a fantasy spot filled with a personal fabricated environment.
ex: I use to use the city room as my pentehouse, complete with dining room, a kitchen, a sunken living room with a fireplace, and large glass coffee table. Even now, Brandy and I have a room which we call home,... it is personal and no other is invited to go there.
Situational Date RP is the nest phase in my order. Create a date,... make it elaborate and a bit beyond the normal lines of straight sex. Example: I setup a date with a friend for a weekend in San Francisco, using my knowledge of the city to share on a downtown walking tour. It was a lot of fun sharing points of interests with my friend and gave her a chance to get a description of the types of shops about a core area I use to stay in. When we found an Scottish/Irsih heritage store, things got interesting, especially when I started trying on kilts
up to this point you are staying being yourself... responding to different scenarios... but still playing yourself.
Taking that next step is a challenge playing as a character. you might keep it simple to start with, put yourself into simple situational roles. 2 office co-workers,..., housewife and handyman. A police officer...
When you find a compatible partner then you may attempt something more elaborate. A story of substance which does not at first deal with a more complex story. Weave it together, spontaneously towards that payoff (the sexual encounter)
Doing so you might find yourself able to chain a deeper story line:
example: A partner and I set up a scenario involving an office party. There was an elaborate weave of distracting her husband, a boss who was horny for his subordinates wife... a hot office sex scene. We chained that further... the co-worker taking the wife and her drunk husband home, screwing in the living room while he was passed out on the couch. Another scene where I had spent the night instead of going home, and she slipped into the guest room, the following morning in the kitchen stealing a moment while breakfast is cooking and is distracted with his morning preparation, the later a blackmail attempt... the office sex was caught on video and the boss attempted to extort favors from the wife...
I think that immersion into a total fabricated world as Momma Andrea describes is the high end of such play. Can you create a fantasy world, elaborate enough to chain events and characters throughout. To me it is the high end of RP.
We are chained only by our limits of imagination, free it and it will take you to some marvelous experiences.