One of the more popular muscle mass building programs that is being used right now is the 5X5 program. Essentially this workout is designed to hit your muscles hard three times per week and then allow enough time to promote growth and recovery. It was designed for strength athletes because one of the most common effects seen by it is an increase in strength.
It should be noted too that you should have a good deal of base training behind you before starting a program like this. The intensity and volume are higher so if your body is not used to dealing with higher loads it is going to wind up having a hard time recovering and you could risk overtraining.
What the 5 X 5 program specializes in is periodization, which is changing the program as you progress through it to constantly change the stimulus, promote increases in strength by further challenging your muscles each week and then also having enough recovery time built in with an easier week so as to not become overtrained.
You are basically going to complete the 5X5 program for a total of 7-9 weeks, which includes 4-6 weeks of prep work and then a 3-week peak phase. After you have completed the full cycle it is a good idea to do a deloading week where you workout with less intensity or if you prefer just take a week for complete rest.
During the first week of the training program you should error on the cautious side to make sure your body has a chance to grow accustomed to this type of training. It is likely going to be something you aren't used to so you need to allow for adaptation to take place.
Choosing Your Weight
During this week you will pick a weight that you can do for a total of 5 sets with 5 reps. This weight shouldn't be so easy that you feel you could do a lot more than that but likewise it shouldn't be so hard that you are not able to complete the given protocol.
One of the most essential factors of this program is that you do in fact do 5 sets of 5 reps. It is a key factor in the success of the program and must be followed.
Before starting the first week it would be a good idea to set a 5 rep max for each of the exercises (as described later) so that you know what weight it is you are specifically trying to beat. During the first week you want to use a lesser weight since obviously you do have 5 sets to complete rather than just the one you used for your rep max test.
Bumping It Up
If after the first week you have managed to successfully complete all your sets at a specified weight then bump it up 5-10 pounds for the following week. Again here, if you bump it up and are not able to successfully complete all the reps with proper form then this is too high of an increase and you need to be more moderate.
If you have really been struggling to lift the amount of weight you were using however then you will want to keep it the same for one more week and then hopefully after that you can raise it higher.
By the time you hit weeks 4-6 you will hopefully be setting new rep maxes and will be seeing a significant increase in strength, provided you are in a caloric surplus. You can sometimes still see strength increases even if you are in a deficit however it is much more unlikely, especially among advanced individuals.