I could write a three to four hundred page treatise on how to firm up the buttocks, receive an award or special mention for the same, and an academic kiss from a cute fitness instructor. But let’s start with physical activity and forget about the cute instructor.

I work a lot on my buttocks and legs: without strengthening the leg muscles it will be almost impossible to firm the buttocks. But there is also a problem: the glute exercises that are often done in the gym involve the hamstrings and quadriceps more easily than really the glutes .
It is no coincidence that the nightmare of many women is to have sturdy legs and flat or uncooperative butts and no, not all sportswomen have fabulous butts.
Difficult to find exercises that isolate only the glutes, minimizing the work of the quadriceps and hamstrings. It is also difficult to be able to involve all parts of the buttock.

A self-respecting training plan in women must include at least half an hour of work on the buttocks twice a week, for a total of three exercises per session, if we want to have firmer and more protruding buttocks in a short time.
Those who run, for example, if they understand the shots in the run , should have a fabulous butt, instead with the normal uniform jog they work the leg more (yes that flap flap jog that I see some of my friends do and that gave them calves very big, but no results at the level of the buttocks: here, if you want to know something about how to firm the calves I will put you in touch).

But stop the chatter and let’s move on to how to firm up the buttocks. Here are the exercises that I recommend. 
Squats with a balanced weight and   lunges : I suggest 4 sets of 8 to start, and as you increase the load for the squat go down to 4 sets of 5 reps. There are many types of squats. Personally, I find bodyweight squats with a barbell or sumo squats with pause, using a dumbbell, enough. What does it mean to pause. It means being squatted for three seconds before going back up.
Traditional lunges involve more the quadriceps, but if we try to stretch the legs as much as possible we will also involve the buttocks, and in any case the variations are endless: with a step, while walking, with a barbell, with dumbbells; the exercisebridge or bridge on the ground (bridge, in order to be successful you must raise the pelvis well up, contracting the buttocks, and foresee at least two other variants: the first is to put one leg over the other, and lift yourself up with only one leg , called one leg bridge; the other, which I use and which makes me work a lot, in addition to the classic bridge on the ground is the use of a stool or a chair on which to place the feet: this variant, however, involves more the quadriceps ). Once you have become familiar with bridge, I suggest the use of a weight to be placed on the pelvis and finally a barbell to be loaded progressively. After each set, which can be 4 by 8 , stay with the buttocks raised and contracted in isometry for about 15 seconds.
An exercise similar to bridge is the hip thrust : it involves sitting up, with your back against a sturdy bench, and a barbell at pelvis level. The legs must be stationary, the pelvis must be raised first until the back is also raised. Again, contraction and then down, in a sitting position. I guess you didn’t get it a damn thing. But here’s a  very useful video.
Finally, the deadlifts . You must also have a barbell here. You start with an unloaded barbell to learn the technique (or with two dumbbells) and only gradually add weight. These are the exercises you need to ask your personal trainer!
Learned these, with the appropriate variations, you will no longer waste time behind the press or the gluteus machine expecting a miracle.