How does a NPN 2N2222 transistor work?
This may be a common emitter config but it seems that he's trying to test whether the npn is good or not, sorta like a go - no-go test, which is more like a comparator (saturates the npn). May I suggest a simpler circuit?  You dont need two supplies, just a +9V battery. Assuming the LED lights up with ~5mA, you'll get 1.8V to 2V drop across the LED.  So the emitter resistor should be 1K, and tie the collector directly to +9V. When the button is pushed, the 100uA or so of base current will be sufficient to make 5mA or so of emitter current.  You'll get 5V drop across the 1k, 2v across the LED, and the npn will be in sat. You might want to add a 1M resistor on the base to gnd (to ensure npn is off when button is not pushed).