Recently, the story line on LOST has become somewhat confusing to some people. (Okay, maybe not so recently for a lot of people). However, I as always am here to help you because this is truly one of the best shows ever and if you're not watching it, you're missing out.
So first, go grab seasons 1-4 and watch them. Then watch season 5 online. Go ahead, I'll wait.
Okay, so this whole time travel thing has people upset. "What happened originally?" they want to know. When Sawyer wasn't there to save Amy, what happened? The answer, of course, is that Sawyer did save Amy. That's the way it happened. If you don't believe me, think about her baby's name: Ethan. Was Ethan around before Sawyer went back in time? Yes. Could Ethan have been around if Amy died? No. Sawyer always showed up to rescue her.
Still confused? I can make this simpler. Don't think of the timeline as a whole, think of each person's life as a timeline. Like this:
Sawyer is born -> Sawyer sees his parents die -> Sawyer grows up to be a con man -> Sawyer goes to Australia, returning on flight 815 -> Sawyer crashes on the island -> Sawyer goes through lots of bad stuff -> Sawyer goes back in time -> Sawyer saves Amy -> Sawyer becomes a member of the Dharma initiative -> etc...
Amy is part of the Dharma Initiative, married to Paul -> The Others show up and kill Paul -> Sawyer shows up and kills the Others -> Amy goes on to marry Horace -> Amy and Horace have baby Ethan -> etc.
And of course Ethan:
Ethan is born in 1977 -> Ethan leaves the island at some point to become a doctor -> Ethan recruits Juliet and goes back to the island -> Ethan pretends to be a survivor of 815 -> Ethan is found out and kidnaps Claire -> Charlie kills Ethan.
You see, each person's life only flows forward. Even though part of Sawyer's life is lived in 2004 and part of it in 1977, he's still always moving forward through his own personal timeline. I hope I've cleared that up for you all. Go forth and enjoy LOST!