This is a somewhat simplistic explanation but the most natural remedy for gout is an adequate intake of water. Historically it was assumed that alcohol and rich foods caused gout directly. Leaving alcohol aside for a moment, certain foods, it is true, are high in purines (the building blocks of uric acid: think game meats, organ meats, tinned fish etc). Your body needs to be able to get rid of those purines. Some folks are, unfortunately, genetically over-efficient at producing uric acid through metabolic processes ( simplistically referred to as over-producers). Others might have reduced kidney function and not adequately eliminate the uric acid from their bodies (likewise referred to as under-excreters).
Regardless, the amount of uric acid in your blood and thence your joint fluid eventually exceeds its solubility and it precipitates out of solution into needle like crystals which cause severe, painful inflammation in the affected joints (commonly but by no means exclusively, the big toe) and possibly other nasty things like kidney stones. Aside from those drugs and other (arguably) popular remedies mentioned above which either hamper metabolic conversion of purines to uric acid (like allopurinol) or increase the rate of excretion through the kidneys (like colchicine) the other critical factor is fluid intake.
Most people, gout sufferers or not, do not drink sufficient water. Those with gout don't drink enough water to keep the uric acid concentration in their joint fluids below the level at which uric acid precipitates out of solution. Alcohol, coffee and tea are diuretics and cause the body to excret more water than the amount which was imbibed in the first place. Who hasn't woken up with a dry mouth and dark yellow urine after a beer or three?
Historically alcohol (or coffee etc) was often considered incorrectly to be the culprit but it was in fact the dehydration caused by drinking alcohol and eating salty foods without adequate water replacement.
Water, simple, cheap and natural but not necessarily effective in all cases. Allopurinol, colchicine and other prescribed remedies will always have their place in gout management.