I think to enjoy Skyrim you have to enjoy Roleplaying, because that's the main strengh of Skyrim.
Come up with a backstory for your character, give them a short history and a summary of personal feelings, prejudices, etc. (I once played a Kahjit with a fear of water, for example, so anything that involved travelling through water was out of the question unless there was no other option.)
Giving them a D'n'D alignment [http://en.wikipedia.org/wiki/Alignment_%28Dungeons_%26_Dragons%29] or roleplaying as a character you know well helps (e.g. play as Batman, or Kratos, or Zoidberg (Why not?) )
Don't use your knowledge of the game to influence your character's actions, let them choose based on the personalities you gave them.
The greatest character I ever made was a wood elf, he was supposed to be a Robin Hood type character; Chaotic Neutral, who had a personal bone with the Thalmor and no Imperial/Stormcloak leanings.
I began by not following the guy at the start, but by going my own way, since I was very independent, and ended up in Falkreath, where I was immediately lambasted by a stormcloak for being an elf, I stole all his possessions and littered them around the town, did some more petty stuff and ended up getting run out of town by the guards.
Went to Whiterun (still hadn't begun the main quest at this point) and met with the companions, joined them because they looked amoral and cool, and ended up getting embroiled in their questline, which led to a lot of massacres of people for very thin reasons, which was quite an evil thing to do. On the search for coin I ended up in Markarth, and helping out a poor dude got lambasted by the stormcloaks (again) so at this point I decided my character didn't like them, ended up killing a guy in self defence and became accidentally complicit in luring a monk to his doom, was told by a possessed lady how much I loved eating people (and I was a Wood Elf, so her prophetic insistence that this was true convinced me I had cannibalistic tendencies) Then I was thrown in jail and had to break out by "becoming an animal" and killing others without provocation, allying with an insane wildman.
From there I realised that my supposed Robin Hood character was actually full on Chaotic Evil. He had killed in cold blood so many times, had massacred large groups of people for very little reason, was cannibalistic and just downright crazy. This happened because I let the character make those choices, and they all turned out to be awful choices. He became my evil playthough even though I had no intention at all of playing a bad character when I made him.