Partying - Alcohol
If you like to drink - Black Rock City is the place to be.
First and foremost, alcohol (also caffeine and some drugs) will speed up dehydration. That combined with impaired judgment is a deadly combination so get into the habit of drinking water along with your alcohol.
Hangovers on the playa are nasty in a way that is hard to describe, but it is one playa experience you definitely should try to avoid. By the time you are drunk to the point where a hangover is likely, you will probably be partially dehydrated and will be even more so by the time you sleep it off. You are in an environment that is already stressing out your body, and when you crawl out of that sweltering tent all queasy and feeling like shit - that sun will feel like the eye of God (or Sauron if you prefer) trying to bore a hole through your brain.
Drinkers generally have their preferences regarding the poison of their choice. On the playa some things work better than others. Although a cold brew can really hit the spot, consuming lots of beer will have you spending more time walking to the JOTS than anything else (remember you will be consuming a lot more water as well). Generally hard liquor is a better choice when out and about. Like the Holy Grail, choose wisely.
A strategy that works for me is beer when I'm in camp and a flask of straight bourbon or vodka when I'm away from camp.
Although in the default world mixing a lot of different drinks will often make you sick, there is something about the playa that negates this - call it playa magic for lack of a better explanation. Most days on the playa I'll have dozens of wildly different drinks and suffer no ill effects, something I wouldn't dare even attempt in defaultia.
If you are a drinker, consider how much you would normally drink in a day of heavy partying. You will want to have spare booze to offer guests, gift to you favorite bar, etc... so double that and multiply by each day you will be on the playa. Remember you can't buy more at the burn. Any remaining can be donated to the DPW during exodus (they construct BRC and will be there for weeks more breaking down and cleaning up).
There are many bars on the playa ranging from small side street "pocket bars" to huge placed theme camp bars. Like everything else they are free, but this does not mean they are obligated or required in any way, shape, or form to gift you a drink. When you walk up to a bar, engage the bartender in conversation. Human interaction is what bars are all about in BRC so leave that default world transactional attitude at home.
If you find a bar you like and spend a fair amount of time there - consider gifting them something. Ice is always needed and unopened mixers are usually welcome too. Most bars won't turn away booze, but usually have more need for ice and mixers.
Carry A Cup
Carry your own cup everywhere you go. It will get you more drinks and it is proper etiquette. Should you forget or lose your cup and a camp is nice enough to serve you anyway - take the trash with you. Leave no trace means they have to cart out all the garbage you leave in their space.
If you look younger than 40, expect to get carded. Yes, I know it's a hassle but from what I understand they can get a 1,000.00 fine for serving minors. If you do get asked for ID, be pleasant about it - those folks giving away their booze are only trying to protect themselves - especially since the LEOs have been known to set up stings to catch bars serving minors on the playa.
Driving while intoxicated will get you busted just like in the default world. The LEOs are there and they are watching. This includes the line to get through the gate. Do not even crack a beer until you are at your camp and parked for the week. At night the LEOs use night vision gear to watch for suspects - don't be stupid. The other side of this is that driving under the influence is extremely dangerous in a pedestrian city and legal implications aside - you really don't want to be responsible for ruining someone's burn or even killing someone.
2014 Addendum - Beer Choices
In the default world I drink mostly IPAs so I loaded up with them for the burn. What a mistake! Much as I hate to say it, PBR tastes much better in playa conditions although I normally don't like to drink it in default. Think about light and refreshing rather than heavy and bold tasting. Your mileage may vary of course.