The most tried and true way of gaining size is getting stronger muscles.
There's a well known saying:
“A stronger muscle is a bigger muscle”
While I don’t entirely agree with that statement, it is undeniable that getting stronger will aid in the process of your muscle growth.
When you're starting out, the name of the game is getting stronger via progressive overload.
This is slowly increasing the weight you use to force the muscles to adapt; ultimately inducing muscular growth to accommodate the heavier weight.
Typically, muscular progression is dictated by how strong you get on compound lifts, as this builds the foundation of your physique.
Although, when you should increase the weight can become unclear.
As a general guideline, you want to increase the weight by tiny increments each time you reach 12 reps without going to muscular failure.
For example, if you can do 185 pounds on the bench press for 12 reps without needing a spotter, then the weight is too light and you need to increase it.
You will then use that increased weight until you can rep that weight for 12 reps.
Rinse and repeat.
By progressively overloading the muscle in small increments on a consistent basis, you can accrue a huge amount of muscle size and overall strength.