You should always do some research before going anywhere. Learn the local customs (including dress code, tipping, and bargaining), a few words of the local language,currency exchange rates, if there are ATMs, how to use the public transportation, what areas/sights you want to visit, dangers, holidays, etc.
You don't want to plan too much, but having a few things figured out ahead of time can be super helpful when you first arrive somewhere. Determine how to get transportation from the airport (or wherever you're arriving) to an area with cheap hotels. Even better, book the first night's hotel in advance so you know exactly where you want to go when you land. You can always ask the hotel the best / cheapest way to get to there. Also make sure you know if there are functional ATMs at the airport or where you will be able to get local currency.
I highly recommend the Lonely Planet guidebooks for maps, transportation schedules, what costs to expect, etc.
Don't Prepare Too Much
Be flexible and don't limit yourself by trying to stick to any kind of schedule. You never know what you are going to run into and you want to be open to any unexpected experiences. This also gives you the option to move on if you don't care for a certain place. A little structure can be okay, but you will enjoy the freedom of taking it as it comes.
SE Asian countries (and even countries such as Italy or El Salvador) are much more modest than western countries. It is best to only wear bathing suits or short shorts at the beach. Any time entering a church/temple, legs should be covered, and especially women should wear long sleeves. Also when in a temple, you shouldn't point your feet at the Buddha. Watch the locals to see if they take their shoes off when entering somewhere, then do the same.
Americans have a reputation around the world for being loud and demanding. Don't expect things in the country you're visiting to be like they are in your home country. Schedules are not as strict, nothing is as clean, and at times you may have to supply your own toilet paper. Be easy-going and go with the flow.
You should ask before taking anyone's photo. You'd be surprised how many people do not want their photo taken and some people can get downright angry if you try to snap a shot without permission.
Pointing with your finger is generally considered rude. You have to get used to using a waving motion with your hand or other creative method to get your point (ha ha) across.
Some SE Asia tidbits: It is a criminal offense to make negative comments about the King or other members of the royal family. It is impolite to touch someone on the head.
What to Bring
The best advice is PACK LIGHT. Really, one small bag should be plenty. Besides, you will be experiencing a simple life and won't need much, right?
You will be carrying your luggage from songthaew, to ferry, to bus, etc. and sometimes it must be done quickly. Therefore, it is also a good idea if your bag is either a backpack, or something with a shoulder strap. Depending on the coutrny, there's not always a lot of opportunity to roll your luggage.
Take into consideration where you will be traveling to and what is considered appropriate dress for that area.
Read Packing 101
See my Packing List
Although many people in other countries speak some English, most are by no means fluent. If speaking English to someone, try to speak very slowly and use simple words along with hand signals.
You very well may get a smile and nod to just about anything you ask, so beware that all answers are not always correct. You may want to ask the same question to multiple people.
A little local language goes a long way. The locals love it if you at least try to speak some of their language. It shows effort at least. Learn to say Thank You, Hello, Excuse Me, and a few other essentials. It can be very helpful when trying to pay for things if you learn the numbers 1-10.
There are money exchange counters at most airports but I found it easiest to use ATM machines everywhere. You get a good exchange rate and don't have to worry about getting ripped off. Sometimes the currency exchange counter will change one of your large ATM bills into smaller denominations for you so you have money for the bus. Saying something like "Can you make small please?" should work.
Tipping is not part of every culture. Do not tip if it's not the culture! Not only do they not expect it, but you will be setting a precedent for other travelers if you do this.
Bargaining is expected in most countries. Even for hotels if staying multiple nights. Two little tricks that help when bargaining: Near the end of your bargaining, have the amount of money you want to spend out in your hand and offer it. If they see the money, they are more likely to want to take it. Also the walk-away. If you can't get to the price you want, walk away. If they are willing to take your price, they will call you back. Also, if you bargain down to your asked-for price, then be prepared to buy the item. It's bad form to bargain, get your deal, then not make the purchase.
Even if a country accepts US dollars, pay in the local currency. You will not get a good exchange rate otherwise and will ultimately end up paying a lot more for your purchases.
When shopping or doing anything, have small bills on you. "Small money" is key. Don't use it when you don't have to. Use larger bills any chance you can such as in a grocery store, for park entry, etc. Not only do you need smaller denominations for buses and street food, but nobody ever has change - even the busiest of places miraculously don't have any change for you.
Food & Libations
I have very good luck with the delicious locals foods wherever I go. Like anywhere, avoid anything that looks like it has been sitting out. Most food is cooked fresh either in a restaurant or at a street stall. Hand signals work well for not getting something too spicy. There is a lot of GREAT food here, so don't be afraid to try something new.
When choosing a local place to eat, go to the one that's full of locals, not the empty one that the locals don't want to go to.
Drink only bottled water that has not been opened. It will be available everywhere. Also use it for brushing your teeth.
The local beer or booze will always be cheaper than an imported alcohol. Sometimes MUCH cheaper.
Most countries other than the US have great public transportation! Don't be afraid to use it. It is so much better traveling as the locals do. You will see the real day to day life and it is much more interesting than taking a private taxi.
If taking a taxi of any sort always preset a fare or agree to use the meter. Make sure you stress that it is the price for everyone in your party and NOT per person. For women riding a motorcycle taxi, it is customary to ride side saddle which is surprisingly easy. If you ever need to flag down a taxi, don't wave your hand up in the air, just lift palm-down out to the side and kind of pat the air.
In some places (i.e. Bangkok), the public buses and the river taxi boats barely stop for people to get on and off so you really have to run and jump on as well as be ready for your stop. If you miss it, just stand near the front and get off at the next one.
More typical than not, you will not pay the bus driver. Just go find a seat and the bus helper will come collect money from you. If you are not sure how much your fare will be, try to watch what the locals are paying. You have a better chance of being ripped off if you ask how much the fare is. Just give them money and act like you're waiting for change. If they don't have correct change, you might not get it until later.
Depending on time and finances, the night trains are awesome for getting around the country. You can get to your next destination while sleeping and not spending money on a hotel!
Ask for help, constantly. If you are at all unsure of which bus to catch, where to wait for the boat, if you are even on the correct train, ask someone. Or ask a few people as you may get different answers depending on their level of understanding. There are friendly helpful people everywhere.
How many web sites get to have a section on pottys? Just a few things here. Paper does not go in the toilet is most countries! Usually if there is a bin next to the toilet, you should put your paper in it. It takes some getting used to, but just fold your paper in on itself and put it in the waste basket.
On the chance that there's no TP and you forgot to bring your own, there may be something like a sink sprayer to use instead. It can be quite an experience. ;)
It's true that some cultures use their left hand to clean themselves with. Hence you are supposed to only eat with your right hand if you don't have utensils.
There are a few different styles of toilets in SE Asia. It seems the higher the price of the hotel, the more 'western' the toilet. There are some western flush toilets, and there are some western toilets where you have to scoop water from a big bucket to flush it. Then there's the traditional squat toilet which is a p