The basic idea:
Jason is Lois's son with Superman, not Richard.
The story and ending:
While Superman went on a five-year mission to find Krypton, Lex took the time to study extensively the properties of crystals and woo a very rich dying widow, who leaves everything to Lex when she dies, including a very expensive yacht with helicopter hangar.
Lex steals the father crystals from the Fortress of Solitude. His plan was to use a crystal to create his own continent which would break through most of the Eastern Seaboard, including Metropolis, killing many people, and later create real estate for him to extort to the world. Lex also combines one of the father crystals with a piece of Kryptonite, so that Superman could not destroy his new landmass.
Lois Lane (Kate Bosworth) gets herself and her son Jason into trouble again by investigating Lex's home, because of a blackout that Lex caused while experimenting with the father crystal. With Lois Lane and her son kidnapped on his yacht, Lex fires a missile into the Atlantic Ocean, not too far from the east coast, and another Fortress of Solitude-like landmass begins to form, expanding at a geometric rate. At some point, Jason exerts a powerful amount of energy, indicating that he is Superman's son (in the movie).
Lois's husband Richard (Jason Marsden) and Superman save Lois and Jason from the sinking yacht after Lex, his goons, and his girlfriend Kitty (Parker Posey) escape in a helicopter. Lois, Richard, and Jason, get away in Richard's seaplane as the yacht sinks.
Superman flies to the forming landmass and confronts Lex, but is soon weakened by the Kryptonite radiation inside the crystals. Lex and his thugs take the opportunity to get physical revenge on Superman for all the years of torment they suffered in prison. Lex finishes Superman off by stabbing him with a kryptonite shard, breaking it off in Superman's back so he can't pull it out, and Superman falls off the ledge into the water below.
As Superman is about to give up, Lois saves him by getting Richard to fly to Superman's location. She manages to get the shard out of his back with a pair of pliers. Superman uses what is left of his powers to fly past the stormy clouds over Metropolis into the stratosphere, where the Sun revitalizes all of his powers, and then some.
Superman jets back down to Earth, and heat visions his way to the very bottom of the core crystal deep inside the Earth. He lifts up the continent, high above the waters. Lex Luthor knows that he has been foiled yet again, and leaves on his helicopter with Kitty. Kitty's conscience finally gets to her, and she dumps the rest of the father crystals so that Lex can do no more harm with them.
Though the kryptonite core is weakening Superman, once he gets the continent past the clouds, the sun gives him enough energy to raise the entire continent into space, where it floats away from Earth as a very exhausted and unconscious Superman plummets back to Earth. The world is saved once again by Superman, despite a moment where it seems he may have died in the hospital.
Elsewhere, on a very small deserted island, the helicopter has run out of fuel, leaving Kitty and Lex to survive on their own.
Finally, back in Metropolis, Lois attempts to write an article entitled "Why the World Needs Superman." In Jason's room, Superman speaks to his apparent son Jason while he is sleeping, repeating verbatim what Jor-El said to him as he approached Earth years ago. Just before Superman leaves, Lois asks him if he will be around. He tells her he'll "always be around," and flies off into the credits.