Since diodes conduct current in only one direction, they can be used as an AC Voltage rectifier. Take a look at the picture below.
A triangular AC voltage is connected to the input terminals of the rectifier. The output voltage will be measured across resistor R1. When the upper input terminal is positive, there will be a current flow in the diode and the resistor. This current causes a voltage across R1. Assume the peak voltage is (plus and minus) 9V, and the forward voltage of the diode is 0.7V. The peak current will then be (9V - 0.7V)/1k = 8.3mA. The maximum power dissipation of the diode will be 0.7∙8.3mA = 5.8mW.
When the voltage at the upper input terminal becomes negative, the diode is reverse biased blocking the current flow. Since the diode has a very large resistance, all the voltage will be across the diode. This should not exceed the maximum reverse voltage.
So if you want to perform this experiment, you'll need a diode with the following requirements: the maximum forward current must be 8.3mA or higher; the maximum power dissipation must be 5.8mW or higher; and the maximum reverse voltage must be 9V or higher. Any small signal diode will meet these requirements. The resistor can be a regular 0.25W resistor since the maximum power dissipation is (8.3mA)2∙1k = 69mW.
The circuit above is called a half wave rectifier, since the ouput contains only the positive half of the input. The circuit below shows a full wave rectifier.
This circuit works as follows. When the input signal is positive, the currents flows from the upper terminal, via diode D1, resistor R1, and diode D3 to the lower terminal. When the input signal is negative, the currents flows from the lower terminal, via diode D2, resistor R1, and diode D4 to the upper terminal. Notice that the current always flows in two diodes: either D1 and D3, or D2 and D4. This means that the output voltage will always be about 1.4 volts (two 'forward voltage drops') less than the input voltage.
The circuit D1...D4 is called a bridge rectifier. When you look at a bridge rectifier, you'll probably see something imprinted like 'B80C5000/3300'. The number after the 'B' indicates the maximum (reverse) voltage, in this case 80V. The number after the 'C' indicates the maximum peak/continuous (forward) current in mA. In this case the maximum peak current is 5A and the maximum continuous current is 3.3A. Smaller bridge rectifiers only indicate the maximum voltage and current, e.g. 'B40C800'.