Many users have had trouble getting the nRF24L01 modules to work. Many times the problem is that the 3.3V Power to the module does not have enough current capability, or current surges cause problems. Here are suggestions:
Use the RF24 Library from TMRH20 (below) and set power low to minimize power requirements:radio.setPALevel(RF24_PA_MIN); Space the two radios about a meter apart. After you have things working, and if you know you have enough 3.3V current (up to 250 mA or more) then try higher power. The possibilities are:RF24_PA_MIN, RF24_PA_LOW, RF24_PA_HIGH and RF24_PA_MAX
Connect a 3.3 uF to 10 uF (MicroFarad) capacitor directly on the module from +3.3V to Gnd (Watch + and - !) [Some users say 10 uF in parallel with 0.1uF is best] This is especially important if you are connecting the module with jumper wires. Or you are using the regular Arduino UNO which provides only 50 mA at 3.3V
Use a YourDuinoRoboREDArduino UNO compatible, which has an added 3.3V regulator (But add a .1 uF capacitor on the radio module).
There are also nice low-cost base modules like THIS (RIGHT) that you can plug nRF24L01 modules into. These have a 3.3V regulator built in, AND good power bypass capacitors. You can also find these on Ebay etc. They make it easier to get started and keep operation reliable.
If you design a printed circuit board that the module plugs into, add .1uf and 10uf capacitors close to the GND and 3.3V pins. See the schematic of the base board shown on the right onthis page. as an example.
These instability problems are particularly noticeable when 3.3V power comes from a UNO, MEGA, Nano etc. that has only 50 ma of 3.3V power available. Newer boards like the YourDuinoRoboREDhave 350 ma or more available and can run even the high-power modules directly.