Led switch transistor
 

I’m looking for the quickest and simplest way to operate a small red led using a to92 transistor as a switch to turn it on when power is present and off when no power using a 3.7v battery.

Back in the good ol' days Radio Shack used to sell these little Engineers Notebooks. You can probably find these on ebay.

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I mean if the LED and transistor are being powered by the device they're checking for the presence of power in you don't need a transistor at all ...just the proper current limiting resistor in series with the LED, then connect the pair across the voltage source.

I can do that but it would be hooked to the battery and it would stay on all the time what I want to do is when the charger is plugged in the led comes on then pull the plug and it goes out it’s just an indicator to show power in.

Depending on the charger circuitry you could do like Tom says by putting the Led before the battery.

Can’t do that it’s a usb plug, usb charger trying to put a circuit between the plug power in and the battery.

2 rectifier diodes (using a low forward voltage shottkey on the battery is advisable)where one end of each diode goes to the charger and the other end of one feeds the battery and the other end of the other feeds the LED will do the trick.
Camper vans will do this so that the alternator can charge both the engine battery and the separate living quarters battery but when they engine is off the living quarters battery can be run dead without affecting the charge of the engine battery.