How much voltage to give my IR LED?

As with any LED, you should be concerned with the LED current, much more than its voltage.

The voltage across any forward-biased LED (any diode, really) will be governed by the diode, and will only vary slightly with current.

Look on the LED's data sheet for the recommended operating current, or, failing that, the Maximum Recommended current. If you can only find a Maximum Recommended current, operate the LED at 80% or less of the Maximum.

You normally control the LED current using a resistor in series. The resistor value is calculated by subtracting the LED forward voltage from the supply voltage, then using the resulting voltage and desired current in Ohm's Law.

-----------------------Added, after the OP added vital data---------

With 3.3 Volt Vcc, the Atmel ATMega328's recommended output current seems to be 10 mA or so, so you can't drive the IR LED directly from an I/O pin. Instead you will have to do something like:

^{simulate this circuit – Schematic created using CircuitLab}

The 18 ohm resistor should limit the LED current to about 80 mA - safely under its maximum rating of 100 mA. 20 or 22 ohms would reduce the current a bit more, if you want to be safer.

The transistor's emitter must be connected to the Arduino ground.

I'm pretty sure that there are multiple answers on this site with the information that you require.

But: decide what voltage you want to run the LEDs from. Subtract 1.5V - you now know the voltage across the series resistor that you need.

Now divide that voltage by the desired current. If you divide by Amps, you get the resistor value in Ohms. If you divide by mA, you get the resistor value in Kilohms.