What is interesting about the Rest-Pause method is that it can be used for two distinct training purposes.
You can use it to increase your muscle size, known as hypertrophy and it is for this reason that it is very popular in bodybuilding and fitness modelling circles.
Rest-pause can also be used for strength training, and as such is popular with a completely different demographic of gym goer.
Obviously, there is nothing saying that you can't use both rest-pause methods effectively in your programming, this article will look into how best to do that.
Rest-Pause for Hypertrophy
The desired outcome for this form of training is to give you bigger muscles.
The usual range of reps for Hypertrophy is between 8 and 12, possibly as high as 15. You need to be performing each contraction of the muscle perfectly, and through the full range of motion.
What you are going to do is find a weight that you could normally perform between 8 and 10 reps on (with good form). Then you are going to perform these reps until you cannot manage another rep.
Your form should never drop below 85% (perfect form being 100% obviously), if it does then stop!
Rest for 10 to 20 seconds and then start performing reps again. Take another 20 seconds rest and then repeat a third time.
Theoretically you could keep doing this again and again but it would be unlikely that you would be able to do so with such good form. Remember the quality of the reps will always be more important than the quantity.
Why this helps increase muscle size is quite interesting. Your muscles are made up of muscle fibres. These fibres are grouped together in bundles and they are controlled by Motor Units, when you perform a contraction the majority of the required Motor Units will signal their fibres to contract.
These Motor Units are known as low-threshold. Your muscles won't require all of the Motor Units to contract however, the ones left are the high-threshold Motor Units. This is where discussions over slow and fast twitch muscle fibres can come in to play, but for the sake of simplicity we will ignore this.
Now obviously the more fibres you contract, the more your muscle will be worked. The more your muscle is worked the more fibres need repairing and replacing by Muscle Protein Synthesis.
So it is a good idea to get more fibres activated. This is why rest-pause is so good. It exhausts all of the low-threshold Motor Units and begins to recruit the high-threshold Motor Units.
Rest-Pause for Strength
The desired outcome for this form of training is to get you comfortable lifting a bigger weight, say you've been lifting 90kg for 4 sets of 6 and you want to progress to 100kg for the glory of saying you bench a hundred.
But you've never managed more than 4 reps on 100kg before, nothing wrong with that but if you only did 4 sets of 4 you wouldn't be reaching the same level of volume as before. When you were lifting 90kg you managed a total volume of 2,160kg (90kg x 6 reps x 4 sets) but when you did 100kg you only managed a total volume of 1600kg (100kg x 4 x 4).
This is where Rest-Pause comes to the rescue, in this scenario you lift 3 reps (keeping some energy in the tank) rest for 10-20 seconds and then manage 3 more.
Now you have a set of 6 reps, do the same for all 4 sets (possibly having to increase the amount of rest-pauses as the sets progress) and your total volume has increased to 2,400kg.
Your muscles will have worked harder, and have had to adapt to the overload which means that your muscle fibres will be more damaged.
So when Muscle Protein Synthesis occurs your body will create bigger and stronger fibres to replace the old ones.
Slowly you will adapt to the stress and be able to perform 100kg with less pauses, until you can manage it without any.
Considerations for performance
As has been mentioned previously, adding Rest-Pause to your training can force your body to recruit more muscle fibres per exercise, this is going to lead to more muscle damage.
While this is crucial for growth, it also means that you will experience more Delayed Onset Muscle Soreness (DOMS) than usual .
This also means that you will need to increase your protein intake (if you haven't done so already) as your body will need the extra protein to fuel Muscle Protein Synthesis .
Also, improve your sleep quality, and perhaps take a day off from training afterwards as your body will need to recover (as it would for any high intensity activity).
 Schoenfeld, B., Contreras, B. 2013. Is Postexercise Muscle Soreness a Valid Indicator of Muscular Adaptations? National Strength & Conditioning Association 35(5): 16-21
 Hoffman, J., Ratamess, N., Tranchina, C., Rashti, S., Kang, J., Faigenbaum, A. 2009. Effect of protein-supplement timing on strength, power, and body-composition changes in resistance-trained men. International Journal of Sport Nutrition and Exercise Metabolism 19: 172-185