I'm learning Opamps as well and I hope that some of this is correct.
By regular LED I will assume that its a Standard 5mm. Typically it will have a Maximum current rating of 20mA . LED's can and will draw more current than they are rated for if you do not have a limiting resistor in series with the LED and the source.
First off you will need to know 2 things . The voltage you will operating the LED and the maximum suitable current your LED will operate at. In your case the source is the output of the OpAmp that you have chosen for your experiment.Lets choose a current that is below 20mA to be on the side of caution.Lets say 15mA. You can fine tune that to your liking later.You need to measure the output voltage of your Opamp .
Use this formula to find a suitable resistor .R = (VS - VL) / I
R is the resistor value .
VS is the voltage source ( the output voltage of your opamp you will need to measure the voltage at the output ).
VL is the LEDs forward voltage ( different colors of LED have different forward voltages. Typically Red: ~2V,Amber: ~2V,Yellow: ~2V,Green: ~2.5V,Blue: ~3.5V,White: ~3.5V)
I is the current you what you want your LED to run on.Less than 20mA for 5mm stardard LEDs is best.
Now the source (your Opamp) Lets look at the Data sheet which can be searched very easily.
https://www.onsemi.com/pub/Collateral/MC34071-D.PDFLook at page 4 At "Output Voltage Swing" .The output swing is relative to the supply voltages.We want to know how much resistive loading can be put on the output and still have it function properly.
LEDs are diodes and do not have a linear resistance the same as a regular resistor. But for the sake of simplicity lets assume that the LED has A zero resistance and we'll just use the resistance of your limiter resistor in series with the LED we discussed earlier .
So if you have,for example ,a 2k resistor you can see VCC = +5.0 V, VEE = 0 V, RL = 2.0 k ohm and Out put voltage swing is 0.3 V .
Ohms law V/R=I 0.3/2000 = 0.00015A = 0.15mA Not enough to power a 15mA LED and keep the Opamp stable.
Although it says that the opamp has a Output Short Circuit Current of 10mA -30mA that won't guarantee stability.
If you used a small transistor to pass current that is controlled by the opamp then you can light your LED.
If I have anything wrong here then one of the more experience folks here are very welcome to correct and/or comment. I'm learning as well so any extra information would be beneficial.