LEDs are current driven. The current passing through a LED is directly related to the voltage across the LED. eg,for white LEDs, at about 3.6V, you will have 20mA passing through the LED and at 4V, the current will be about 30mA. The 4V, 30mA combo is the maximum recommended values for white Nichia 5mm(size) LEDs.
Resistors in your application will be used to reduce the voltage going to the LED. Lets say that you want to power three white LEDs in parallel from a 6V source. 1)We know that the max V that should go through the LED is 4V.The resistor is therefore required to reduce the voltage by 2V. 2) since you will be powering 3 LEDs in parallel, the total current draw will about(30mA *3) 90mA. To calculate, you divide the difference in voltages (V in -V required by LED) by the total current in Amps. ie, 2V/.09A= 22ohms .
If the 2.2V/ 20mA numbers Inretech quoted is correct, then, as he said, you can put two red LEDs in series to get a total V requirement of 4.4v. You will need the resistor to drop the battery voltage by only 1.6V. Since the LEDs are in series, the current passing through one must pass through the other and therefore only 20mA will be required. To calculate, Vin- V required/ current. ie 1.6V/.02A= 80ohms.
Series/ Parallel. If you hook up 4 AA cells in series, you will have a total of 6 V comming off of the negative and posative ends of the line of cells. Here, the +ve of cell 1 touches the -ve of cell 2, which touches the +ve of cell 3 which (as you can see the trend) touches the -ve of cell 4. In series you add the individual voltages to get the total V. The 6V is measured between the -ve of cell 1 and the +ve of cell 4. If you hook up the same 4 AA cells in parallel, you will have all the negatives connected together and all the posatives connected together. The total output voltage will be 1.5V. The V remains the same, however, the 4 cells in parallel will last approximately 4 times as long as a single AA cell.
With LEDs, series/ parallel connections are the same. In series, you connect the -ve of the first LED with the +ve of the second which connects to the -ve of the third etc.In series, you add the individual V requirements of the LEDs to get the total V requirement. eg, 3LEDs in series will require about 4V *3 = 12V to power them.They will however only need 30 mA from the V supply. In parallel, you connect all the posatives together and all the negatives together. Here, the V requirement for the 3LEDs will be the same 4V however, the current requirement will be (30mA*3) 90mA. Makes sense?