Frodo did not kill Sauron
Sauron did not die. It was said he put most of his power into the Ring, and thus when it perished, he was vanquished, but he did not actually die.
He concentrated within the Ring a great part of his own fëa (soul). In this way, Sauron's fate became bound to that of the One Ring. If it were damaged or destroyed, so too would be Sauron's strength and power.
- From the LOTR wikia.
Notice, nothing was ever said of him being destroyed or killed. I can't find the exact quote in the books yet, but there was a particular passage by one of the Wise Ones that said, if Sauron regains the Ring, he will have power to cover all the land in a second darkness, the ending of which cannot be forseen by anyone. But if the Ring is destroyed, he will lose most of his strength and power, and will diminish and his rising again can never be foreseen.
So no, it is not correct to say Frodo killed Sauron, because Sauron did not die. He was Maia before his corruption, and even at the end of the Third Age, he was still considered a being not of the lower order (the Elves, Men and Dwarves we see). He is still 'alive' as far as we know.
Gollum, aka Smeagol helped (though unwillingly) to destroy the Ring, and was one of those to find it in the first place)
It was Smeagol's friend, Deagol who fell into the river while the two were fishing at least 500 years before the events of The Fellowship of the Ring. He saw the Ring and retrieved it, and Smeagol, enamoured by the gold, strangled his friend to death and hid the body, taking the Ring for his own. After being kicked out of his home, he went to the Misty Mountains, where the Ring abandoned him just in time to meet Bilbo, who took it out. Smeagol (Gollum, by then) accused him of stealing the Ring, his Precious, as he called it.
After the Fellowship broke at Parth Galen, Frodo and Sam went through Emyn Muil, where they met him, Gollum having stalked the Fellowship since Moria. Partly out of fear of being beheaded by Sting (Frodo's sword), he agreed to help the hobbits to Mordor. Along the way, he betrayed them and turned up again in the end at Mount Doom. Frodo did not want to destroy the Ring at the very end, but Gollum attacked him and bit his finger (with the Ring) off. At that point, (in the books) Eru Illuvatar intervened and Gollum tripped of the ledge, taking the Ring down into the Cracks of Doom and getting it destroyed, along with himself. In the movie, Frodo fought him and he fell. Doesn't really matter. Point is, without him, the Ring would not have been destroyed in the end.