The term 'soundproofing' is rather misleading, because in most real-world situations, you can cut down on leakage but you can't get rid of it altogether. Sound isolation is a more accurate term.
The simplest way to attenuate sound is to put a solid wall in its way -- the more solid, the better the isolation you'll get. As a rule, if you double the mass of a wall, you halve the amount of sound transmitted through it. Unfortunately, sound isolation tends to fall with frequency, so even though you may be able to get the mids and highs under control, the chances are that you'll still be able to hear the bass drum and bass guitar thumping away from outside. That's why when you walk past a club, all you can hear from outside is bass.
To give you some examples of what to expect, a single brick wall might have a quoted Sound Reduction Index (SRI) of 45dB (this is averaged over a range of frequencies, so the bass-end isolation will be rather worse than this figure) while a domestic panel door might only give you around 10dB of isolation. Because the degree of sound isolation depends largely on mass, lightweight solutions such as partition walls work noticeably less well than solid brick or concrete. However, there's another useful fact we can utilise -- two walls are always better than one.
If a single wall can reduce the sound leakage by 45 or 50dB, you might imagine that two separate walls spaced apart might give you 45dB for each wall, or 90dB altogether. Sadly, unless the walls are separated by a large distance, the air between them couples energy from one wall to the other and reduces this figure considerably. However, and this is the important bit, two walls with an air gap in between will always give better results than a single wall of double the thickness. The wider the gap, the better the sound isolation, especially at low frequencies.