When approaching acoustic treatment for a home studio, you should consider two aspects: reflections and resonance.
Reflections are caused by hard surfaces and can make a room sound echoey or fluttery. They blur the sound your hear. Reflections are best addressed by using mid-high frequency absorbers in places where the sound will bounce from your speakers to your ears via a hard surface. A good way to start is to mount them at ear height, starting with positions where, if you mounted a mirror, you’d see a reflection of your speakers (when you’re sitting in your listening position). Don’t forget the wall behind your speakers.
Resonance is caused by the shape and dimensions of the room. It usually causes a room to sound boomy or muddy. Room resonance cane make it extremely difficult to judge bass and lower mid balance accurately. Other than changing the dimensions of your room, resonance is best addressed with bass traps and other LF absorbers placed in corners and edges. If you’re on a budget, other semi-solid absorbent items can work – such as mattresses, cushions, etc. Anything reasonably dense, but still has some ‘give’. Keep in mind, though, that unlike mid/high frequency absorbers, it takes a *lot* of material to make a significant difference.
Furniture or other large objects can also be useful. Anything that breaks up hard flat surfaces will make the room’s reflections more complex and irregular. This might not reduce the overall reverberation in the room, but will make it more pleasant and natural. For a listening room, it’s not as good as absorbers, but it’s better than nothing. For a recording room, it might be better than absorbers if you want a more ‘live’ or bright sound.