Fib ratios are based on dividing successive numbers in the sequence 1,1,2,3,5,8,13,21,34,55,89,144,233,377,... where each term is the sum of the previous two terms.
Critical Fib ratios are obtained by dividing any term by a near term, e.g.
233/377 = 0.618 = 61.8%
144/377 = 0.382 = 38.2%
89/377 = 0.236 = 23.6%
377/233 = 1.618 = 161.8%
377/144 = 2.618 = 261.8%
or their square root, e.g.
SQRT(233/377) = 78.6%
Also, 0.5 (50%) is considered to be an "honorary" Fib ratio
These ratios are plotted as either retracements (38.2, 50, 61.8, etc) or extensions (161.8, 261.8, etc), from arbitrarily selected swing highs and lows (i.e. where the 0.0 and 100.0 are set at the high/low prices on these candles).
Occasionally prices reverse (i.e. local tops and bottoms are formed) at the Fib retracement points. The "art" is knowing which swing highs and lows on which to base the Fibs, and then which key ratio (38.2, 50, 61.8 etc), to select. Fibo proponents (including Elliott wave students) believe that Fibo retracements are predictive; skeptics suggest that if we plot enough lines on a chart, prices will reverse at some of these, simply due to coincidence. However, everything else being equal, they can be used as profit taking points during exit, giving one a debatable technical edge.
Like other chart patterns and technical indicators, Fibos are capable of creating a "self-fulfilling prophecy", i.e. if enough heavyweight traders believe that a reversal will occur at a certain point, then they will place their own buy/sell orders accordingly, thereby causing the hoped for reversal. IMHO that is what their proponents are counting on.
Personally, I find their predictive value (in terms of accuracy) to be overrated: a significant problem being that if several lines are being plotted, at which one will price actually reverse? However, when trading pullbacks in trends, I have learned that many retracements occur somewhere between the 38.2 and 61.8 levels, hence I use them as a rough estimate in placing orders, specifically if there is a suitable candle pattern (hammer/shooting star, railway tracks, engulfing pattern, morning/evening star, etc) straddling, or very near to, the retracement level.
MT4 has its own in-built Fibo retracement and extension indicators. You can add any price retracements/extensions to suit your requirements.
Daily pivots are calculated as the average of the previous day's high(H), low(L) and close(C). Support (S1,S2,S3) points and resistance (R1,R2,R3) points are calculated according to the following formulae:
This is the basic method; there are also Camarilla and Woodie methods. There are also "midpoints" (labelled M1, M2, M3, etc) which lie exactly half way between each of the above points.
Since forex is a continuous 24 hour market, the cut-off point for each day is arbitrary, although many traders seem to use either 0000 GMT or 0000 EST New York.
Weekly and monthly pivots can be calculated in similar fashion, using weekly/monthly high/low/close.
Pivots were apparently invented by floor traders many years ago to forecast potential future S/R levels. Apparently there are automated entry systems that use them today, to generate entry orders. Proponents include Peter Bain of www.forexmentor.com
However, my experience is that pivots are less reliable than Fibos in forecasting possible turning points. Again, skeptics suggest that if we plot enough lines on a chart, prices will reverse at some simply by way of coincidence.
Attached are my preferred MT4 daily pivot calculating indicators. Preferred because they calculate prior days' pivots (allowing us to gauge their usefulness, in terms of forecasting), and also allow a variable cut-off point.
Confluence between Fib ratios, pivot points, diagonally drawn trendlines and/or prior S/R (horizontal lines drawn through previous points of reversal or congestion) can improve the possible predictive potential, i.e. the greater the confluence, the greater the likelihood that more proponents will use them (once again, the "self-fulfilling prophecy" concept). One benefit of both Fibs and pivots is that their values are less dependent on timeframe, i.e. because local highs and lows remain constant across near timeframes, whereas with moving averages or other technical indicators, these change immediately one shifts timeframe. Hence Fibos/pivots are more "fixed", and their predictive value is debatably greater.
The above is my simplistic explanation. I suggest you do a Google, use the FF search engine, and/or go to free forex education sites like www.babypips.com for more comprehensive info.
The previous post is quiet clear on what Pivots and Fibs are.
I'd just like to add that a Fib level is support/resistance of recent price action. Pivot Points are support/resistance of the daily market.
The most important thing about the two is when they both agree; and this does happen quite often. If your swing high and swing low fib retracement points to a Fib Extension that over laps a reversal Pivot Point... that price level will be a very important exit opportunity.