If you want a very complete synopsis of all the characters, songs, tales, places and much more go to
www.glyphweb.com/arda aka The Encyclopedia of Arda. It is completely chock-full of information about most anything you could ever want to know about the Hobbit, the Lord of the rings and the silmarillion.
Heres my summary of Frodo before the quest to destroy the ring.
Frodo was born on September, 22 2968 of the third age, to Drogo and Primula Baggins. When he was a young hobbit, his parents were "drownded" in a boating accident. He lived with the Bucklanders, until his uncle Bilbo adopted him when he was in his tweens (his twenties, which is like the teenage years to us humans). Bilbo and Frodo share the same birthday, so when Bilbo was turning 111 Frodo was celebrating his coming of age, at age 33. This is the party as seen in the movie. Where Bilbo disappears and leaves to go stay with the elves in Rivendell and leaves Frodo to inherit Bag End. He also leaves the ring to Frodo. I think it's 17 years later that Gandalf returns to Bag-End and tells Frodo the truth behind the ring. Frodo makes up his mind to leave the Shire and sells Bag-End to the Sackville-Bagginses. He tells them he's moving to a house in Crickhollow, but he actually starts his journey of leaving the Shire. Merry, Pippin, Sam and Fatty bolger are all in on his plan to leave the Shire. Fatty and Merry are the ones who make all the arrangements, I think.
I don't remember exactly what happens after he leaves hobbiton so I'll leave someone else to cover that.