Appliances plugged in GFCI outlet works but when plugging in the downstream outlet doesn’t
Only do the following if you are familiar with electric wiring and the necessary safety precautions. 


Switch off the circuit breaker that controls the outlet with the GFCI.
Open the outlet and remove the GFCI. 
Check the wiring. 


There should be two wires (black and white) going to the terminals marked LINE.  There should also be two wires (should be black and white) connected to the LOAD terminals.  The hot wires are black and the neutral wires are white. 

If these check out, and if you think you are prepared, then switch the breaker back on and check the voltage at the LINE terminals (should be about 120 V). 

Then check the voltage at the LOAD terminals (should be the same voltage). 

Push the TEST switch on the GFCI.  The voltage at the LOAD terminals should
 go to 0 V while the voltage at the LINE terminals should stay at 120 V.

If all of this checks out, you need to check at least one of the downstream outlets. Again, they should have a black and white wire connected to their terminals and the voltage should be 120 V.

Trip the GFCI and check that the voltage goes to 0 V.

Note that if any of the connections use the backstab (located at the back of the outlet), you should change those to connect with the screw terminals on the outlet. Backstab connections are known to be unreliable. 

If everything checks out, then you may need to call an electrician.