Richard White doesn't belong to the mainstream of the DC-Universe. He was created for the movie Superman Returns and was played by the actor James Marsden who played also Cyclops in the movies X-Men, X2: X-Men United and X-Men: The Last Stand. He was created by Bryan Singer, Michael Dougherty and Dan Harris.
Before the movie
Richard White was hired as a reporter for the Daily Planet by his uncle Perry White. Lois thought he was only hired because of his relationship with Perry but Richard stated that his uncle is no fool and he was hired because he's at what he's doing. Richard thought, that the whole Superman stuff is old news and Lois need to be the great reporter again. They worked together and than Richard kissed her. A short moment after, Lois kissed Richard back and they ended in a romantic relationship.
Storyarc (The Movie)
Richard White is the nephew of Perry White and worked as a reporter for the Daily Planet. After Superman left the Earth, he married Lois Lane and take care of her child Jason White. It's unknown if Jason is the son of Richard or Superman but he's likely the son of Superman.
After Lex Luthor kidnapped Lois and Jason, Richard tried to rescuing his wife and his kid but they were caught within the kitchengallery of Lex' ship. Superman gets there and saved them finally. But after he saved their lifes, Superman was stapped by a Kryptonite dagger and fall into the ocean. Together, Richard and Lois could safe Supermans life and took him on the board of Richards aquaplane. After Lex' plan failed, Lois still ended up with Richard.