Trouble with very first circuit
The LED voltage, current, and resistor equation will be (3v - 1.5v) / 30 ohm = 0.05 A (or 50ma), so your calculation is correct.

To troubleshoot this measure the voltage across each component when the circuit is powered, across the battery should be 3v,  then 1.5v across the resistor, and 1.5v across the LED.  

If the LED shows 3v it may be connected in reverse, or is burned out open.  

If the LED shows near 0v it may be burned out shorted.  

(Note that the voltages might be off a slight bit as the LED forward voltage at 50ma seems to be nearer to 1.4v per the forward current chart, see data sheet page 6).

Also be sure to observe the warnings in the data sheet about eye safety.  These LEDs are bright and emit concentrated light, even though they are infrared they can still be dangerous to look at directly.