One of the simplest and most effective exercises you can try at home to work your legs and glutes are lunges. It is a simple exercise, and you can try many variations to avoid getting bored.
Stand straight, with your legs open to the width of your hips. Take a long step with your right leg forward and bend both knees until they are at a 90-degree angle (your left knee should almost touch the ground). To return to the starting position, push with your right leg. It is a unilateral exercise, so you must do it with both legs, alternating one and the other.
You must keep your torso straight to avoid injuries.
The easiest way to give more intensity to this exercise is to add external weight by using a bar with discs placed on your back, a weighted vest, or a pair of discs or dumbbells attached to both sides of the body.
You can also do several repetitions with the same leg and short moves up and down without completely going up. Do the same with both legs.
Lunges can also be made backwards, a movement that has a greater involvement of the glutes at the moment of returning to the initial position.
Another variant that achieves great intensity is the jumping lunge (to be performed without an external load). Perform the strides alternatively with each leg, and switch between them with a jump. This requires good muscle work and balance.