You will need to add up the current for the following:
- the number of LEDs that will be on at the same time (say 3 for this example)
- what the Arduino needs (no idea, but guess at 30mA)
- Any other devices that will be running (seems none)
So (3*20)+30 = 90mA. You power supply must be able to supply 100mA.
You will need resistors to drop the voltage 'across' the LED to 3.3V. So if your Arduino is running at 5V, you need to drop 1.7V for the LED to see the right voltage across its terminals. Using Ohms law V=IR or R= V/I =1.7V/20mA = 85 Ohm. Pick something bigger like 120 and you will should be fine.