assuming you can use a multimeter and assuming you know what transistors look like then:
Assuming you know if the transistor is NPN or PNP, and assuming you know where B, C, and E are, then just test the B-C junction and the B-E junction as if they were standard diodes. if one of those junctions is a "bad diode", then the transistor is bad.
Also, check the resistance from C to E using a higher Ohms scale (say, the 2 Meg scale). Be sure your fingers don't touch the metal test points or you will just measure your skin resistance.
If the transistor is good, you should get an open-circuit reading from collector to emitter. NOTE: the above assumes silicon. With germanium transistors you may measure a high resistance from C to E.
USING METER TO SEPARATE NPN FROM PNP
If you have a transistor but you don't know if it is NPN or PNP, then you can find out which it is using your Ohm-meter if you know which lead of your meter is positive.
Assuming you know where C, B, and E are on the transistor, do the following. Connect the positive lead of your Ohm-meter to the base. Touch the other lead of your meter to the collector. If you get a reading, the transistor is NPN. To verify, move the lead from the collector to the emitter and you should still get a reading.
If your meter reads open-circuit, then connect the negative lead to the base and touch the positive lead to the collector. If you get a reading, then the transistor is PNP. Verify by measuring from base to emitter.
THINGS TO WATCH FOR
Some transistors have diodes from collector to emitter built into them. They will not read open-circuit when measuring resistance between C and E.
Some transistors have resistors from base to emitter built into them. They will read that resistance when measuring Ohms B to E.
Some transistors are Darlingtons. They have a higher reading base to emitter which may appear as an open on a VOM.
CHECKING TRANSISTORS IN CIRCUIT
With power disconnected from the circuit, you can try some of the above measurements on transistors that are in the circuit. However, your readings can be deceptive due to resistors and other components in the circuit. You can try disconnecting the base lead from the circuit before making measurements. Be sure to reconnect it after testing.