you can pretend to sleep in a bed you can get ontop of with /playdead
Step 1. Find the RP community.
Step 2. Ask them for advice.
Step 3. Ignore naysayers and prepare to be heckled (set those users on ignore).
Step 4. Probably through heavy usage of emotes, having a character profile fleshed out may help .
Step 5. Look for RP UI add-ons.
Step 5a. Understand that your character and other characters may conflict with the lore and may be inconsistent, find a place where you can minimize that (be courteous to other RPers).
Step 6. Give back tot he community.
Hmm, i think logging off while at an inn, you'll just have to assume your character is going to bed right then and there. Its all "real time" - and this includes the sleeping. If you play, your character is awake and when you don't - he or she is either high on skooma, or taking a nap.
EDIT: And about how to roleplay. I usually bump into people, and am quite lucky to find them (roleplayers) - you can also ask about joining a RP Guild in chat while in game, or visit forums.
And just like the person above me said, just type /playdead - and your character lies on the ground indefinitely, as many emotes are looped (which i love) - its kinda like a sleeping animation.
Or better yet, just use the /sleep emote...
Edit:
I usually do what I can to find an RP community. I admit, despite being an RPer, if I try to RP whenever in game I start feeling silly when it is clear no one else is.
If you don't mind being seen as a bit weird, then you can develop your character's personality (or even a template and let the character grow as you play through the game) and just... act it out! It's like acting impromptu in theater. Play the character how you think they would act. When you interact with others, state opinions on the quests, or even refuse to do some if you think they are wrong. Chat with NPCs or mumble something about incompetence. Just act it out!
Please you have no soul, you should sleep like a corpse!
Also: Feel free to ignore that little tid-bit. I mean, hundreds or thousands of people without souls! How impractical! Like how in GW2 I ignored the whole of the main story for my charr. She was not part of a warband and joined a human noble-house as an inventor... She got weird looks.
Emotes are a great way to roleplay. If you like roleplaying in single player games, you're going to absolutely love it in an MMO setting; as other players will interact with you, opposed to the mechanical AI you're used to.
You can sleep on a bed with /playdead, /sleep1 or /sleep2; for a much larger list of emotes, here; http://elderscrollsonline.info/news/list-of-emotes-is-revealed
For me the MMO part of the RPG just allows more RPG. I will have three fighting characters and three support characters.
I have already had my Dark Elf Sorc mine a whole pile of iron ore, after running into a really rich section of Ash Mountain. He also scored a pile of nice heavy armor and a nice one hand sword on a couple of quests and put the whole lot in the bank. My Redguard DK and part time Blacksmith took all this out, used the armor, and used the iron ore to make ingots to make the two pieces he lacked. The sword was a pretty big improvement too. Went out and tanked a boss that kicked my ass before. I mean tanked, he could not kill me and eventually he went down. I was very happy, the tank thing had been eluding me.
For fighters: I will have an Imperial DK or Sorc Tank with Daggerfall. A Dunmer Sorc in the Pact and a Kajiit Nightblade in the AD.
For support: An Orc Templar Blacksmith Woodworker in Daggerfall, an Argonian Nightblade Clothier and Provisioner in Morrowind and an Altmer Sorc Enchanter and Alchemist in the AD.
well you did kick down the gates of soul harbour there a bit~
I'll have to try a Coldharbor speed run.
Here's that fabled RP community you want: http://teso-rp.com/
Recommend you look at a lot of their sticky threads for info on MMO-RP.
Have fun!