Well I want the the LED's to function as bright as possible, without damaging them. So would in series be better than in parallel like I have them now? Also how can I find out what type of resistor I need without using these online calculators?
LEDs have a turn-on voltage which is a minimum voltage that the LED needs before it will turn on. If you stack LEDs in series, the voltages needed to turn them on add up.
So, if you have two LEDs that both need 3.5 volts to turn them on, you will need 7 volts to turn them on in series.
You only have 4.8 volts, so you can't put them in series or none of them will turn on.
Calculation:
As a first step, have your 4.8 volt battery and a 3.3 volt LED. The difference between these voltages will appear across the series resistor. So, it will have 1.5 volts across it. 4.8 - 3.3.
For a current of 0.5 amps, this resistor should have a value of 1.5 volts / 0.5 amps or 3.0 ohms.
At this current, the voltage across the LED will rise to 3.4 volts, so the resistor must have a value of 1.4 volts / 0.5 amps or 2.8 ohms.
Your battery will rise to 1.35 volts per cell or 5.4 volts when fully charged, assuming NiCd or NiMH.
So the resistor would then be (5.4 - 3.4) / 0.5 or 4 ohms.
For a current of 1 amp, the calculation is similar and the voltage across the LED is now 3.5 volts:
So the resistor would then be (5.4 - 3.5) / 1.0 or 1.9 ohms.
1.8 ohms is near enough. Don't go any smaller if you can't find 1.8 ohms.
5 watt resistors are not as cheap as 1/2 watt ones, but much cheaper than high powered LEDs. The power is actually about 2 watts, but it will run hot, so a bigger rating would be better.
I would try one LED with a 3.3 ohm resistor, for a start.