Plan on a long day preferably earlier in the summer to take advantage of long daylight. Stay the night before and leave early (before sunrise) Plan on using the Huts for water resupply so no need to lug a lot up Madison. North to South is generally regarded as easier. Do the car spot the night before, if possible spot a second car at the Cog for bail out.
Most important, you need to have good weather conditions. It has snowed every month of the year on Washington and sustained exposure to precip along with inevitable winds can be dangerous. If the forecast for the region is bad find somewhere else to go. Generally the forecast lags for the summit ridge, if there is a chance of clearing in the forecast for NH, the odds are the summits are in the clouds as they are the last to clear.
One minor addition, take you time at the beginning, many folks set too fast a pace up Madison from Valley way and regret it later in the day. Unless you are trying to set a record you are better off starting at a slow pace. As Tim mentions its easy to spend way to much time on the top of Mt Washington and Lakes of the Crowds (although I must admit, Lakes usually has some great goodies for sale).
