The idea of Purim is that we are supposed to see the hand of God in everything. Purim was a נס נסתר, it could easily have been explained away as coincidence etc., yet the Jews realized that it was all from Hashem. A person who has true בטחון is a happy person. he doesn't let things bother him because he knows that everything is from Hashem even what seem to be problems/difficulties. It is like the old story about the guy who is rushing to catch a plane and just misses it, he gets really upset. An hour later he hears that the plane crashed. At that point he realizes that it was for the best that he missed the plane. We are supposed to view everything in life that way. Someone who is drunk isn't bothered by anything and therefore we get drunk on Purim to reach this state (even artificially) of not being bothered by lifes problems.
There are a number of caveats to the mitzva of getting drunk:
1. The mitzva is only during the day, there is NO mitzva whatsoever to get drunk on Purim night and therefore it is no different then getting drunk on any other night, e.g. assur.
2. According to many Rishonim the mitzva is only with wine (see the Rambam, Rashi in Megilla and others). Therefore anyone who drinks hard liquor is not mekayem the mitzva
3. The mitzva may only be in the seuda. The Rambam clearly holds this way as he puts this din with the halachos of the seuda. The Shulchan Aruch follows in the Rambam's footsteps and put this din in סי' תרצ"ה דיני סעודת פורים
4. The Mishna Berura writes that if you are going to be מזלזל in even the smallest mitva by getting drunk you shouldn't.