Transistors can be damaged by heat when soldering or by misuse in a circuit. If you suspect that a transistor may be damaged there are two easy ways to test it
Testing with a multimeter
Use a multimeter or a simple tester (battery, resistor and LED) to check each pair of leads for conduction. Set a digital multimeter to diode test and an analogue multimeter to a low resistance range
Test each pair of leads both ways (six tests in total)
- The base-emitter (BE) junction should behave like a diode and conduct one way only
- The base-collector (BC) junction should behave like a diode and conduct one way only
- The collector-emitter (CE) should not conduct either way
The diagram shows how the junctions behave in an NPN transistor. The diodes are reversed in a PNP transistor but the same test procedure can be used
Testing in a simple switching circuit
Connect the transistor into the circuit shown on the right which uses the transistor as a switch. The supply voltage is not critical, anything between 5 and 12V is suitable. This circuit can be quickly built on breadboard for example. Take care to include the 10k 
resistor in the base connection or you will destroy the transistor as you test it!
If the transistor is OK the LED should light when the switch is pressed and not light when the switch is released.
To test a PNP transistor use the same circuit but reverse the LED and the supply voltage.
Some multimeters have a 'transistor test' function which provides a known base current and measures the collector current so as to display the transistor's DC current gain hFE
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