He inherits a problem—an evil ring of power—from his uncle, who’s become overly attached to it and doesn’t understand all the problems it can cause (just like the others who previously owned the ring).
Frodo’s given the task of destroying it.
Almost immediately Frodo is trailed by a completely succumbed previous ring-bearer. This creature, known as Gollum, has killed for possession of the ring before and would do it again.
Meanwhile, Frodo is fighting and vowing to not become like Gollum; yet it’s practically unavoidable. The enchantment is too strong.
The insane previous ring-bearer offers to “help” Frodo and his bodyguard, Sam. He’s going to walk them to Mordor for the sole purpose of destroying the ring. But not before carefully triggering some infighting, separating Frodo and Sam, and then leading dazed Frodo into a giant spider’s lair.
At the crucial moment, as he’s about to cast the ring into the fires of Mount Doom, he decides the ring is mine. It would have remained so, but the previous ring-bearer lunges forward and gruesomely steals it—and in the fray, falls into the fire.
After a little drama, Frodo and Sam walk home. Frodo is left with lasting scars, Sam returns to the Shire that he originally left with the sole purpose of protecting (along with Mr. Frodo, of course), and both of them are considered strange hobbits for the rest of their days.