the quickest way is to drink on an empty stomach make sure it is hard liquor like vodka or scotch or whisky from the south
The above is the quickest way to get drunk. I do not advise this technique though. Chances are you will be ill that night or the next day.
For me the best (not the quickest) way to get drunk is with a somewhat filled stomach by drinking a bottle of moderate to good wine. Take your time. Make sure you eat while drinking. Drink a lot of water and have a cracker or two before going to sleep. You will not end up obliterated but you will end up calmly drunk.