To paraphrase the post and lay it out chronologically, since the post itself is long and the additions jump about a bit;
Frodo when speaking with Galadriel has this interaction;
‘I would ask one thing before we go,’ said Frodo, ‘a thing which I often meant to ask Gandalf in Rivendell. I am permitted to wear the One Ring: why cannot I see all the others and know the thoughts of those that wear them?’
‘You have not tried,’ [Galadriel] said. ‘Only thrice have you set the Ring upon your finger since you knew what you possessed. Do not try! It would destroy you. Did not Gandalf tell you that the rings give power according to the measure of each possessor? Before you could use that power you would need to become stronger, and to train your will to the domination of others.’
Frodo here is given the information he needs to figure out how to wield the ring.
Very soon after this Boromir, a man who had been nothing but kind and enduring and who had saved Frodo's life once already, is ensnared by the ring and attacks him. To me, this marks the moment Frodo realises he will likely come to the same end, no one has the will to resist the ring.
Soon after that, Gollum joins him and Frodo acquires the means to essentially practice dominating someone's will. By the time this becomes relevant again it is clear that Frodo knows a great deal more about his charge than he used too and has already made his plan. In sight of the Black Gate, he tells Gollum this;
[In reference to the danger Gollum is in] You swore a promise by what you call the Precious. Remember that! It will hold you to it; but it will seek a way to twist it to your own undoing. Already you are being twisted. You revealed yourself to me just now, foolishly. Give it back to Smeagol you said. Do not say that again! Do not let that thought grow in you! You will never get it back. But the desire of it may betray you to a bitter end. You will never get it back. In the last need, Smeagol, I should put on the Precious; and the Precious mastered you long ago. If I, wearing it, were to command you, you would obey, even if it were to leap from a precipice or to cast yourself into the fire. And such would be my command. So have a care, Smeagol!’
He quite literally describes what happens in the final confrontation, like some books foreshadow their endings and some of them just have the main character tell you what will happen. It makes me so insane.
In my mind this is also Frodo trying to soothe his own conscience here. His words will not reach Gollum deeply enough, Gollum will always choose the ring in the end, but Frodo is still using that compulsion as a means to succeed in his divine martyr's quest, putting the burden on Gollum's body whilst he takes it upon his soul.
Of course, this was all preordained by divine decree, there is no other way for this story to end, which I feel like Frodo is more consciously aware of than many other characters, casting his growing despair and melancholy in a new light. Then, well, it all happens just as foretold;
‘Down, down!’ [Frodo] gasped, clutching his hand to his breast, so that beneath the cover of his leather shirt he clasped the Ring. ‘Down, you creeping thing, and out of my path! Your time is at an end. You cannot slay me or betray me now.’
Then suddenly, Sam saw these two rivals with other vision. A crouching shape, scarcely more than the shadow of a living thing, a creature now wholly ruined and defeated, yet filled with a hideous lust and rage; and before it stood stern, untouchable now by pity, a figure robed in white, but at its breast it held a wheel of fire. Out of the fire there spoke a commanding voice.
‘Begone, and trouble me no more! If you touch me ever again, you shall be cast yourself into the Fire of Doom.’
Then the vision passed and Sam saw Frodo standing, hand on breast, his breath coming in great gasps, and Gollum at his feet, resting on his knees with his wide-splayed hands upon the ground.
The curse is set, Gollum attacks Frodo within the crucible of the volcano, biting the ring off of his finger and thereby sealing his own fate. His celebration at being reunited with his precious sees him slip and tumble into the chasm below.
So, Frodo takes the power of the ring, the very thing that has been drilled into the reader as The Final Failure, an action from which no one can recover, sure to spell the end of the world as every one of the so called 'Wise' will tell it, yet he saved the world in doing so. His soul is sickened for it though, leaving him unable to live in the world as it is any longer, which is the price he pays to do this great heroic deed, the deed he was divinely ordained to do. It makes me sick I tell you, sick!!