Wait, I thought we were going to be prisoners again, of course, but now our characters are supposed to have been sentenced to death? That's news to me.
But in any case, I'd imagine that, like in past games, the crime you commited to warrant your arrest will be left up to the player to decide, though if you're supposed to be scheduled for execution, it seems to narrow it down somewhat, as it can't possibly be a petty crime, still, I'm sure the game won't tell us. Myself, I'll have to see what kind of character I start with before I decide what it will be.
In any case, Cyrodiil's 1000 gold penalty for murder may not necessarily remain in Skyrim. Skyrim can have different laws from Cyrodiil, after all, especially 200 years after Oblivion. And even for Cyrodiil, 1000 gold always seemed like kind of a light penalty for murder. Also, in Morrowind, if your bounty exceeded a certain amount, guards would say you were sentenced to death, but then they'd just try to kill you instead of trying to arrest you for an execution later, obviously, that didn't make it into Oblivion.
He posted on this forum that Oblivion's level scaling was better than Morrowind's.
I think that would specifically involve burning at the stake, myself, going by these forums.
Of course, your character could be accused of feeding trolls.
In which case the person you see being executed is a body-double, or some sort of trick (arranged by the other faction?) to enable your escape.
I'd imagine it's going to start off with you in prison waiting for your execution, and something will happen to give you a chance to escape. Maybe the God of Plot Convenience decides to lend you a hand and a dragon attacks the prison you're being held at, or maybe Esbern or someone else decides to save you, maybe your executioner doesn't do a very good job and you're not quite dead when a Dwemer centurion digs you out of your grave and takes you to a doctor, who knows? Or maybe we already know, but I don't.