Reading this post from Coach, I decided that it might be helpful to clarify some points on how hard to push while working, when to terminate your set, and how to know if you're over-training.
"No brain, no gain" does not mean you can expect to make gains without pain or discomfort. Pushing yourself requires that you fight through discomfort. The key here is that while making gains usually entails some amount of pain or discomfort, you are not guaranteed to make gains simply because you're experiencing pain or discomfort from training. You need some way to tell whether your discomfort is productive. This is where Foundation comes in. Foundation provides programming so that you can be certain that the discomfort you feel while working out is productive. If you're following the programming correctly, the chances that you're over-training are very low.
This does not mean you should ignore pain. It's important to learn to distinguish between the discomfort of hard work, and the pain of a developing injury. When you work hard, your muscles become fatigued. Most people will experience this as a dull 'burning' sensation in the muscle belly. This is the kind of pain that you need to fight through. If you feel pain that is sharp and localized, especially if it's in the tendons or near the joints, that's a sign that something is wrong, and you need to look into it carefully to determine if it's safe to proceed. When stretching, similar advice applies. Heavy stretching should feel similar to light stretching, only more intense. Sharp, localized pain is a sign that something is not right.
So, addressing the topic at hand: how do you know when to stop? The simple answer is that you should only stop when your body fails - not your mind. "No grinding reps" doesn't mean you shouldn't fight. If you're doing ABH and you notice that your arch is dropping and you're getting tired: you don't stop, you fix your form and keep going. If you're almost done with pushups and you're starting to slow down: you grit your teeth, pick up the pace, and press on. If you're doing HBR, and you're sweating like crazy and your abs feel like they're on fire and it feels like every nerve in your body is telling you to stop and rest: you keep pushing. If you're in a bent-arm chin-hang, holding nothing back, fighting with every ounce of strength you have to keep your chin above the bar, and yet your arms refuse to listen to your mental commands; you gaze on in abject horror as the bar slowly rises above your chin: then you can honestly say that you've failed the set. If you stop before the point where you're no longer physically capable of performing the exercise correctly, you've missed out on an opportunity to get stronger.
Ultimately, fighting through discomfort is a skill you learn by doing, not from an essay. So while hopefully this essay will help to clarify what you're going for, the best thing you can do is practice. Keep trying to fight harder. Find or recruit people in your area to work out with, so they can keep you honest. Attend a seminar. Most importantly, keep pushing yourself to do more.