Suffice it to say that in technical charting, the phenomenon of certain key percentages for retracements have proven much more than coincidence. Consider the following chart example.
Here we see an example of several key retracement levels that show up as support or resistance. Notice the two key levels are 38.2% and 61.8%. These actually represent ratios of numbers in the Fibonacci sequence. The 61.8% level represents the ratio a number to the next number in the sequence. The 38.2% level represents the ratio of alternating numbers. While there are many such ratios, these two seem to be key ones. The 50% level also shows up as a support or resistance level, although it isn't often as strong as the other two. For accuracy, it should be pointed out that 50% doesn't actually represent a Fibonacci ratio.
What is interesting to take note of is that the areas that are represented by the key retracement levels were already acting as support levels as the stock was moving down. Notice then in the areas circled that where these levels acted as resistance. In the first case, as the stock begins to retrace upward, it encounters the first Fibonacci level at 38.2%. That level represents 38.2% of the total distance between the high point and the low point marked of by the Fibonacci retracement.
Notice that this level acts as resistance but then is broken. Now the next level is the 50% level. The stock manages to retrace 61.8% of the entire movement before moving back down, ultimately breaking back below the 38.2% level. However, notice as it does that these Fibonacci retracement levels continue to act as either resistance or support levels.
Ultimately, the answer is somewhat speculation. The Fibonacci sequence seems to show up in so many different areas in nature. Perhaps there are psychological levels ingrained in our brains that trigger buy and sell impulses at these levels without our actually realizing it. Remember that support and resistance are simply psychological levels where buyers or sellers are willing to step in.
Perhaps it's a self fulfilling prophesy. We believe these levels to be key levels, therefore we act accordingly when they are reached.
The key thing to remember is that like other forms of support and resistance they aren't guarantees. A support level acts as support until it is broken and then the odds favor a continued move downward to the next support level. Similarly, resistance when broken suggests that the most likely direction is up to the next resistance level.
The hardest part about using a Fibonacci retracement is drawing it to begin with. The choice of starting and ending points is somewhat subjective but generally, the goal is to select extreme levels of a trend. In the chart I showed above, I selected the market high and what was at the time, the market low.
It may help to remember the goal. What we want to find out is that if a stock has moved from one level to another and appears to be pulling back or retracing, how far might it retrace? The answer lies in marking those two levels. They can represent two extremes as show above, or a Fibonacci retracement could be drawn on the subsequent bounce from the lows to the new, lower high. What would we be looking for? The answer to the question: Knowing the stock has made a run from the lows to the new high and seems to be pulling back, where might it pull back to?
Notice on this chart, the 0% level is at the top and the 100% level is at the bottom. We are now measuring the retracement from the high back to the lows.
So that's one of the things to know... the starting point and the ending point. The starting point will represent the 100% level and the ending point will represent the 0% level. Think of it this way... if the stock were to start retracing from its current high and it went nowhere, what percentage would it have retraced? 0% right? If it went all the way back to the lows it would have retraced 100% of the movement.
A Fibonacci retracement can either be drawn from high to low or low to high. It just depends on what you want to measure. The best way to learn to draw them is through practice. Draw them on different points and see what they reveal historically. Then over time your confidence and ability to use them for future support and resistance will improve.