I give it my best shot... But I've only recently gotten back into it (after about a 3 year hiatus). Since I'm just starting back into it, I'm only doing 2 sets of reps, which really isn't enough to give me failure (at the right weight settings). Most weeks, I just concentrate on keeping the same weights and making it through the reps. If I can then easily make it through 2 sets, I'll add a 3rd set. In the 3rd set, I might reach failure.
Your muscles can lift a certain amount of weight repeatedly, but after you do so many repetitions, they get tired and just won't work any more. (It's not so much the burn, but they just won't move). This is failure, and this is why it's dangerous without a spotter on things like bench-press & squats. It's not a matter of pushing through the burn - the muscles have quit on you! At this point, it's not a mind over body thing, so don't think you can be superman and lift that bar off you if you think about it hard enough.
The last time I truly reached failure was in Iaido class. This is a Japanese martial art dealing with swordsmanship. Almost all the positions start from "Seiza" or sitting/kneeling Japanese-style. You raise your butt off your feet, put a leg out in front of you, and essentially do a lunge to stand up. Repeatedly. For an hour and a half or more! Ouch. the muscles would shake, and doing the motion was more and more difficult. During the last 10 minutes of class or so, my legs just wouldn't work in that motion any more! I had to roll over on my side and use my arms to help me stand up.
It's the same idea, though. You should be doing a motion/weight that is a challenge, but you can do (under normal circumstances). But you should be approaching failure around the end of the 3rd set. If you're not, and it still feels really easy through the first 2 sets, (and not too challenging or approaching failure on the 3rd) you might try increasing the weight.
--Janis