Place absorbent materials on all hard surfaces that might reflect stray high frequency waves. Low frequencies diffract or bend around obstacles in their path. Nevertheless, absorbent materials placed in the path of low frequencies will attenuate them somewhat. The greatest reduction in the amplitude of low frequencies occurs when you isolate your bed from the floor. Using thick sound insulating material under just the feet of the bed helps.
Earplugs help to reduce high and midrange frequencies.
This exercise is great for the education of your ears and will make a huge difference in noise reduction. I realize that this step will present problems for most folks not in the audio field. One approach is to use a signal generator or an analog synthesizer to generate a sine tone that you send through a sound system in the space. Sweep the frequency of the sine tone from subaudio through supersonic. On the oscilloscope display try to match up the excursion of the wave at a non-resonant frequency of the room.