Raymond can see/communicate with ghosts. His father had the doctor put him on anti-psychotic medication when he was a child and told him it was for high blood pressure. Raymond and Becca successfully return the little girl's remains to her father and thus giving them both peace in the afterlife.
Raymond's mom leaves his dad for the gardener. His dad has to sell the house and no one likes him. Raymond and Becca open a Supernatural Detective's agency at the end.
A little longer version:
Raymond (Matthew Gray Gubler) can't find work after he graduates from business school. (Which he went to because he father wouldn't pay for college otherwise.) He's a bit of an odd fellow, favoring a big purple scarf and a wild hairdo. He moves back home with his parents, Donald (Ray Wise) and Eve (Barbara Niven), where his dad harasses him regularly about his fashion sense. He goes to the local bar where he meets a bully from his school days as a chubby boy and also Becca (Kat Dennings) a pill-popping bartender who takes a liking to him. (Becca and Raymond even have an epic dance scene.)
As it turns out, Raymond's father had him put on "blood pressure" medication when he was a child which was actually anti-psychotic medication. The doctor hates his dad (as everybody does in the film because Raymond's dad is an a**hole who spouts racist, sexist, and just generally rude things all the time) so when Raymond returned home the doctor told Raymond that he was cured of his blood pressure problem and stopped giving him the medication. Raymond starts to have crazy ghost dreams when he drinks/when the doctor stops the medication. When Raymond starts seeing ghosts again, he's being visited by a little girl who was murdered around 100 years in the past after her remains are disturbed -- first by the gardeners, who take her necklace and then when her remains are sold to the historic society (cameo by John Waters!) by Raymond's dad.
Raymond and Becca return the necklace to the little girl so her father can bury her again and they can both move on in peace. After this Raymond's mom leaves his dad for the gardener, Raymond's dad puts the house up for sale, and Raymond and Becca open a Supernatural Detectives business.