Am I using my multimeter correctly to measure current?
The first thing to do is verify that your equipment works, in a lot of cases measurements that don't make sense can be from measurement error.

First test only the resistor from 9V to ground, you should measure 40mA. 

If not then check the fuse and also check the batteries in a meter, low batteries can give false readings. 

I also see that the LED is not lit, so this could indicate that it may be damaged. It may also be that the LED is backwards which would be a problem. Check the LED with the diode mode on the meter, it should be around 3.5V for the forward voltage. With the LED and resistor you should get somewhere between 20mA and 30mA. And the LED should be lit.