One of the most frequent reasons a good looking set up fails is that the trader only looked at one chart. A perfect bull flag on the daily chart can be very attractive, but if you look at the weekly chart and it's just slammed into a major resistance level after a massive run, the chances of a clean breakout are going to be very much reduced. Multi timeframe analysis is simply the act of looking at more than one chart before you take any action and it's one of the easiest ways to improve your trade selection.
The fundamental concept is that each timeframe tells a different story. A weekly candle is going to represent five days of buying and selling so the structure on that chart is going to be the structure of the larger, slower moving participants. A 1 hour candle is going to represent much shorter term activity. When the big picture and the little picture agree, trades tend to go pretty smoothly. When they're in conflict you're often just going to be in a fight between a short term move and a longer term trend.
The simplest way to think about it is in three layers. The first layer is your trend timeframe which is just telling you the direction you should be in. The second layer is your setup timeframe which is where you actually look for the pattern or level. The third layer is your entry timeframe which you use to fine tune exactly where you get in and where your stop goes. For a swing trader a fairly typical combination would be the weekly chart for the trend, the daily chart for the setup and the 1hr or 4hr chart for the entry. A good rule of thumb is to keep each layer roughly 3-5 times larger than the one below it so that you're getting different information from each.
Here's how that would look in practice. You'd start on the weekly chart and ask the fundamental question: are we in a higher high/higher low situation, are we in a range or are we in a downtrend? You're also looking for the key support and resistance levels and whether price is above or below the 21 week and the 50 week moving averages. If the weekly trend is up you're looking at longs. If it's a down trend you either avoid it or look at the short side. That one step alone filters out a huge number of the weak ideas.
Next head over to the daily chart and look for the actual setup. That could be a pullback to the 21 EMA, a bull flag or a retest of a broken resistance. The point is that the setup has to be in line with what the weekly chart is telling you. A pullback to the 21 EMA in a stock that's also above the rising weekly support is a far better trade than the same pullback in a stock that's actually sitting below a falling weekly average.
Finally go down to the lower time frame to fine tune your entry. The daily chart might show price at support and on the 1 hour you're looking for a break of a little downtrend line or a bullish reversal candle. That's the same concept really. It just allows you to get a more precise entry and a tighter stop, which improves your risk to reward.
There are a few traps to be wary of. The first is checking too many timeframes. If you're jumping around from the monthly, the weekly, the daily, the 4 hour, the 1 hour, the 15 minute and the 5 minute chart you'll invariably find one that confirms whatever you were already inclined to do. Stick to three and pick them before you start. The second trap is allowing the lower timeframe to override the higher one. A 15 minute bounce in a weekly downtrend is almost always just a pause, not a reversal. The third is entering on a lower timeframe signal without first checking where the next key level is on the higher timeframe. A very good looking 1 hour breakout that runs straight into daily resistance has absolutely no room to run.
Conflicts between timeframes are also information. If the weekly is bullish and the daily is in a deep pullback you may not have a trade at all, you may just have a stock to watch. Patience can be the key here as often you'll find that waiting for the daily to turn back in line with the weekly trend gives you a setup with the trend on your side.
To build the habit, add one line to your checklist for every trade. You need to write down the weekly trend, the daily setup and the entry trigger. If you can't fill all three then you don't actually have a trade. After a month or two go back and compare the trades where all three timeframes were in line with those where they weren't. Most people will find the ones where all three timeframes are in line are vastly superior in performance and that in itself is a good enough reason to keep the habit.

