The maximize muscle growth, you need to pay attention to four things: muscle fiber fatigue, muscle damage, mTOR activation, and local growth factors and lactate release.
Here's what each of those means and their practical applications in the gym:
To quote Professor Zatsiorsky, "A muscle fiber that was recruited but not fatigued was not trained." This approach is supported by the work of Cameron and Mitchell (2012) that showed if you train to muscle failure (until you can't lift a weight anymore) the muscle gains are the same over an 8-week period whether you used 30% or 80% of your maximum.
Here we're talking about training to, or close to, failure. With each rep you're fatiguing more muscle fibers and your strength decreases (about 2-4% per rep). This forces your body to recruit more muscle fibers to continue moving the weight. Once you reach failure you've recruited and fatigued a large amount of your muscle fibers and have stimulated them to grow.
For decades, muscle damage was seen as the only way to stimulate growth. Damaging the muscle cells triggers the repair process, which is driven by the immune system and relies heavily on stem cells – they donate their material to repair the damaged muscle fibers and build them thicker.
Muscle damage is best accomplished by using fairly heavy weights (70-85%) for moderate reps (5-8, maybe up to 10 reps per set) on exercises where the target muscle will be stretched under load.
mTOR triggers protein synthesis and initiates the muscle-building process. While every type of resistance training stimulates mTOR activation, two types have a greater impact – loading the eccentric or negative portion of the exercise and having a muscle under significant tension while it's stretched. So we're talking slow eccentrics (4-6 seconds) while contracting the muscles as hard as you can, and flexing the target muscle for 2 seconds in the stretched position.
The burn, or accumulating lactate (lactic acid), has long been associated with muscle growth by bodybuilders. And science has recently shown that they were right!
Lactate itself can trigger muscle growth (Oishi et al. 2015, Nalbandian and Takeda 2016). It increases stem cell activity, increases follistatin and decreases myostatin which leads to muscle growth. A correlation between lactate and MGF (IGF-1) release in muscle has also been found. These local growth factors will directly stimulate protein synthesis in the muscle. These are maximized with a fairly long time under tension (40-70 seconds per set) and, in the case of local growth factors accumulation, keeping the target muscle under constant tension.