If someone knows his body well enough, then using a rate of perceived exertion (RPE) scale works great. You can know what weights to pick and how much fatigue to accumulate across a workout for the desired training response. If you can use it well, it's a very valuable tool. However, in my experience, most people don't know how to use RPE at all.

First, for it to work well you need to know your body well enough to know how many reps you still have in the tank at the end of a set. Second, you need to be able to be honest with yourself in the middle of a workout about how you feel. That gives some people license to slack off, and others the freedom to say, "I had at least 4 more reps in me," on a set where the last rep was the grind of the century.

As an alternative, most people do well with a plan that takes into account daily fluctuations (as RPE does) without allowing for too much subjectivity.

There are several methods of knowing how well you're recovering, and consequently, how hard you should be pushing yourself in the gym day-to-day.

1. Testosterone/Cortisol Ratio. The gold standard is Testosterone to cortisol ratio. If you just so happen to be a biochemist with access to a lab, then feel free to take a saliva or blood sample each day and track T:C. The higher the ratio, the better off you are. Unfortunately, this isn't an option for most of us.
2. Heart Rate Variability Monitoring. The next best option (and still a very good option) is heart rate variability (HRV) monitoring. If you buy some HRV software or app for your phone, it'll come with instructions for knowing how to interpret the data, so I won't wade too far into an explanation of that. In essence, though, what HRV tells you is how dominant your sympathetic (fight or flight) and parasympathetic (rest and relax) nervous systems are. If you're getting high parasympathetic readings, you're in the clear to push hard in the gym, but if you're getting high sympathetic readings, that means stress is starting to accumulate and that you'd do well to back off for a bit.
3. Test Your Grip Strength. Grip strength is another viable option. Grip strength is correlated with T:C ratio and is best assessed with a hand dynamometer (you can pick one up on Amazon for about $30). While they aren't as accurate as measuring T:C ratio directly, they give pretty good approximations of recovery status. To use grip strength as a measure, all you have to do is measure your grip strength daily, at approximately the same time, for a couple weeks during light to normal training to establish a baseline. After that, a higher than normal reading indicates that you're ready to really smash some weight, and a lower than normal reading indicates that you probably need to take it easy for a bit. Use the dynamometer three times with each hand, and then take an average to negate the possibility of a bad test.
4. Monitor Morning Heart Rate. The poor man's version of this type of testing is monitoring morning heart rate, which correlates with peripheral nervous system activity. All you need is a stopwatch. In the morning, before you've gotten out of bed, simply find your pulse and count your heart rate for 60 seconds. Take a couple weeks to establish a baseline, and after that, a high reading means you need a break, and a low reading means you're recovering well.

Once you've got an idea of how well you're recovering, it's time to adjust your program. All you need to do is have a prescribed "step up" for good days and a "step down" for bad days. That way, you won't go too far off base guessing at what you need to do on any given day. For example, let's say you're on a typical 5x5 program. When your T:C, HRV, grip strength, or morning HR readings are normal, you stick with 5x5 for the day.

If T:C is high, HRV is indicating parasympathetic dominance, morning HR is low, or grip strength is high, you know you're good for more that day. Instead of just going 5x5, you could start with a heavy triple, hit your normal 5x5, and finish with a burnout set of 10-15. Conversely, if your recovery barometer is indicating that stress is accumulating, you may want to drop back to 3x3 with your normal 5x5 weight, or drop your training weights by 10% for your 5x5 to allow for more recovery.

HRV programs are pretty good about helping you interpret results, and for grip and morning HR, anything more than a 5% swing is significant. If your grip is 70kg, a reading above 74 means you're ready to tear into extra weight/volume, and less than 66 means you need to take it a little easier. If you normally have a morning HR of 70, it's just reversed -- 66 means you're ready to rock, and 74 means you need to cool your jets.

After you've determined the biofeedback values for "exceptional," "normal," and "recovery" days, it's time to decide how to tweak your base program. This is totally up to you, but in general, extra volume or a couple heavier sets are perfect for "exceptional" days, and a reduction in volume is best for "recovery" days. If you don't feel confident throwing a lot of extra wrinkles in your program, you could adjust 5x5 to 8x5 or 2x5 based on biofeedback, and leave everything else as-is. If you want to be a little more creative, be my guest. Just make sure you know exactly how you're going to adjust your plan.

In essence, this approach gets rid of the learning curve. It allows everyone to train like advanced lifters who have enough experience to optimize their workouts to their daily ability. Instead of learning over a decade of trial and error, you can apply the same approach right now.