How the output of a bicycle dynamo can be displayed using Arduino?
The first thing to look at before you connect the bicycle dynamo to an Arduino is what type of signal / voltage it generates. The link you've provided: http://www.lanzo.se/experiments/dynamo/dynamo.html gives you the answer. It's an AC signal which varies between +4V and -4V (It could be much higher if you spin it faster). On the Atmega328P data sheet under "Absolute Maximum Ratings" it says "Voltage on any Pin except RESET with respect to Ground -0.5V to VCC +0.5V". Obviously, -4V exceeds the -0.5V maximum so don't connect it directly to an Arduino.

The signal from the dynamo to Arduino must be limited to between 0V and 5V (for an Arduino operating at 5V). The answer on how to accomplish this is a general electronics question and should be asked on a different forum e.g. https://electronics.stackexchange.com/questions/132330/8v-ac-signal-into-3-3v-digital-input-pin

The "frequency meter" part of your question is easy to build with an Arduino. You could use an Uno or something smaller like a Pro Mini with a 16 x 2 LCD display and this library: https://github.com/k3ng/k3ng_antenna_tuner/tree/master/libraries/FreqCounter. An I2C backpack for the LCD is only a dollar more and makes the wiring much easier. To use the backpack you'll need this library: https://github.com/marcoschwartz/LiquidCrystal_I2C.