Just watched this for the first time, and enjoyed it immensely. Some here have suggested that there's no 'real' story at all. I don't agree: Lynch doesn't work like that - no matter how bizarre and reticulated, there's a story there, all right, but you have to dig for it.
'Mulholland Drive' informs this film considerably. Having deconstructed that one to my satisfaction, I have a clearer view of how Lynch does things; how he shows us the elements, the language he uses, and what he leaves out for us to discover. So, then - *SPOILERS*, if I'm right:
As with MD, there's a big clue in the first few seconds: Fred is shown in close-up, looking thoroughly wrecked, smoking a cigarette unsteadily. There's a buzzing sound, and light sweeps across his face and the room. *The sound is one you'll become familiar with later, in the jailhouse.* Fred looks up, warily.
Major premise: I believe this scene shows Fred, in the last moments of his life, having his last cigarette before they come to take him to the chair. This may, in fact, be the only 'real' scene in the film, with everything else being Fred's distorted recollection, and the rest a psychotic break fantasy he constructs to escape from his grim situation.
As the door to his cell opens, Fred rejects the awfulness of reality, and transforms the buzz into the sound of his door intercom, and at this point we go into his personal flashback as the story continues.
The acting and dialogue is often stilted and unrealistic in this flashback. What we're seeing is Fred's recollection, which - as he himself says - is not necessarily the way it actually happened. His relationship with Renee is tense and unreal, with lots of suppressed rage. Cleverly, the undercurrents are conveyed mostly by the background sounds - listed in the credits as 'Ominous drones' - and these provide the significance that the dialogue alone would lack.
At the party scene several events take place: his suspicions about Renee and the impossibly sleazy - because he's seen through Fred's eyes - lounge-lizard Andy are effectively confirmed (for him). And he meets the 'Mystery Man', a devil-figure who tells Fred "You invited me (into your home). It is not my custom to go where I'm not wanted". I suspect that this figure is Fred's attempt to unload his guilt onto someone else: a 'devil who made him do it' - don't you have to invite the devil into your house? Perhaps he's the personification of Fred's insanity, or his jealousy. Or all of the above - all the dark influences in Fred's life and head.
As the flashback continues, we see the progression up to the point where he finally does murder Renee, horribly. Again he attempts to reject the reality by showing it all on video, but reality intrudes and a few seconds are shown of him 'really' sitting among the dismembered parts of his wife. His subsequent trial and sentencing are skipped over - they're a blur to Fred - and he winds up on Death Row.
Facing execution, and unable to tolerate his real state, Fred then creates a fantasy in which he escapes his fate by miraculously turning into another person - an innocent: young, enjoying a simple life, good at his simple job; with groovy, understanding parents and a pliable girlfriend.
The scenes around Fred's miraculous replacement are classic Lynch fantasy-made-real: the dialogue is ludicrous; the events comic-book. We see the same in the fantasy world of the central character in MD.
Although safe in this new fantastical environment, Fred/Peter is unable to resist being drawn back into danger, initially via his unlikely relationship with the - again comic-book - gangster boss, Mr. Eddy. This gangster character is a one-dimensional, violent crazy man who recalls the fantasy mafia types invented by the central character in MD to 'explain' her bad break.
Even so, Peter's life will remain peaceful if he avoids any dealings with Eddy outside of the grease-monkey relationship. But Fred's paranoia demands danger, and Peter begins an even less plausible and obviously perilous association with Fred's new incarnation of Renee: the pure-hearted damsel in distress that is Alice.
Except that, once again, Peter's life is contorted by Fred's paranoia, and Alice slowly metamorphoses into a spiteful, greedy psychotic who leads Peter further into danger.
(I looked for the 'Eye of the Duck' peripeteiac scene that Lynch always puts into his films, and one of the candidates is, I think, the moment where Alice points the gun at him after raiding 'Andy's' house. The tableau is held long enough to allow you to contemplate all that could happen if she shoots Peter and takes off. But that's not possible in a Fred/Peter fantasy, so we continue, with the point about her ruthlessness made.)
What else? The storyline continues as might be expected, with Alice now in total control. The cabin we've seen before just prior to Fred's metamorphosis. Alice disappears. The Mystery Man returns, and so does Mr. Eddy and Fred. All of this in a fight, during which the devil-figure hands him a knife that allows him to defeat Eddy/Dick Laurent (as we have discovered), and finally everything turns to crap as Fred heads back onto the highway with retribution on his tail. Things look hopeless, and the escape fantasy has brought him back to the point where he came in.
And then Fred begins another metamorphosis, which we never see completed, and the film ends. Is this another fantasy escape, or his death in the Chair?
I don't know how much of this is correct. Perhaps one day someone will tie Mr. Lynch to a rack, put electrodes on his nuts, and extract the line-by-line details of his wonderful creations. Until then we must wonder and worry. And marvel.