Start looking around your relationship and realize that nothing — absolutely nothing — looks the way it did when you started. All of the little things about them that used to make you smile to yourself when on your way home from a date have been somehow transformed into grating tics that they can't get rid of. Start to notice things that, once seen, can no longer be ignored. Latch onto their more negative habits and pick at them, as you might a scab in a particularly irritating location on your body. Become overwhelmed with the desire to tell them to just stop being… themselves. Realize that that would be ridiculous, and instead swallow your constant frustration like an oversized antibiotic. Feel oppressed by their presence.
Stop being interested in sex. Be repulsed by their touch, even when its offered only in kindness and comfort. Find yourself increasingly tense when you know that sex is expected, and nothing short of resentful at the implication that you should be having sex with them. Know that letting your sex life together wither and die like this isn't constructive for anyone — and it certainly isn't making them feel good about themselves — but feel completely unable to force yourself to fake it. Watch them go through the motions of trying to make things good ahead, like they were before (and be painfully aware of all the connotations that now come with the word "before"), but remain completely indifferent to their affection. Feel nauseas when you see them on top of you.
Realize that almost your entire time together is now spent in some variation of a fight. There are the quiet, seething, passive-aggresive fights; the screaming words we don't actually mean but which feel good to say fights; the bringing up problems that we'd long-since resolved to be spiteful fights; and everything in-between. No indiscretion or slight is too small or too petty not to launch into a tirade, to go back-and-forth until you're apologizing and someone is swallowing their pride to take the blame for this particular scuffle. Be unable to admit that the problem may just be inherent in the two of you together, and not just a series of thousands of tiny injustices foisted upon you by the hands of fate. Consider everything "just a fight", instead of a symptom of a much more profound problem. Blame each other for everything.
Know that the moment is going to come, likely sooner than later, where you're going to have to end this. Dread the conversation the way one does a test that they haven't studied for but which is incredibly important to their overall grade. Run over what you're going to say enough times that every word in the sentence has lost its meaning. Be so tired, so physically tired of fighting that you want to begin nearly every sentence with "I can't do this anymore," but be unable to do so when you go to actually tell them how you're feeling. Understand how much it's going to hurt them, how it wasn't always this way, and though the fleeting visions of the love you used to share aren't enough to make you stay, feel a sharp pain in your stomach when you remember them. Know that the person you once loved with every fiber of you is no longer going to be a part of your life, and feel the emotion of it all like quicksand.
Finally have that one fight that you know is going to do it. Get so angry and, more than that, so exasperated, that you can no longer walk away from this one and lick your wounds. Come to a kind of calm silence in which the clear inability to exist together is far more prominent than any joy you get from spending together. Start to speak the words you've been saving up like bullets inside you for months now, for which you want to soften the blow, but know that nothing is going to make "I don't want to be with you anymore" less hard to swallow. Tell them that you don't want to fight, but that you don't want to make up, either. Stay for their protests, and perhaps their pleading, but be ready at the end to say "no". Though breaking it off on the tail end of a fight, and not in some calm moment in which you both could have collected your thoughts, may not have been the most mature route — it had to end. Repeat things about how hard it's gotten, about how mean you are with each other, and about how you "just can't do this anymore". Hope it sounds as sincere and pained as it actually is.
Know that they will hate you for a while, but know, beyond all doubt and even through your guilt, that you did the right thing.