
In Star Trek, everything that has happened in the show and previous movies stays the same, but Nero drives his ship through a blackhole and kills Kirk's father and destroys his ship, which creates a new timeline running alongside the original one. Nothing from the first timeline changes, the history is all still intact, but basically starting at Kirk's birth, there's a whole other reality where anything could happen. Nothing from the first timeline has any effect on this one (save for Spock slipping through the blackhole and interacting with new Kirk).

The Star Trek timelines did not affect each other except for Spock slipping through the blackhole (but he was smart enough not to do anything crazy). We've yet to see if the Lost timelines have any effect on each other (prior to the bomb going off), but I'd be really curious to see if there is a blackhole situation on Lost in which someone can slip through and have an affect on the other timeline (and though Spock is super logical and didn't mess with anything, I can't see our castaways being so smart).
Point is, I'm really excited to see how all this works out. I find time travel (especially when done well) super fascinating but also incredibly difficult to wrap my head around, which is a lot of fun for me (Primer had me working shit out in my head for days). I'm totally in for the ride.