Get a lot of Q's on this, so I thought I'd put together a post.
First you need a decent digital meter with a diode test function. Forget about using the ohmmeter part of your meter, it is way too unreliable for this. Almost all digital meters nowadays have a diode test included, and it is 100% necessary for even the rudimentary reliable results that we are shooting for here. If you need to buy a meter, remember that you'll get what you pay for. Don't cheap out with a crappy $10 meter from Harbor Freight or something, when from eBay you can get a good used Fluke 77 for $30. You can buy a decent new meter for less than $100.
Just so you understand the basics of the diode function, the reading you get when you use the diode test is the voltage necessary to overcome the depletion layer at the P-N junction of the diode. Don't sweat the meaning of that, I just want you to understand the units of what you will be measuring.
If you grab a plane-Jane 1N4004 diode, for instance, set your meter for a diode test, and connect the positive lead to the anode and the negative lead to the cathode (the side with the band). You should read about 0.45V to 0.65V or so, depending on the amount of current that your meter feeds through the diode. Reverse the leads with positive on the cathode and the negative on the anode, and you should read an 'OL' or 'Overrange'...check the documentation on your meter to better understand how it will indicate an open circuit, but essentially there should be no conduction with the leads reversed. A shorted diode will show '0V' with the leads in either orientation.
Many meters give a short 'beep' to audibly indicate conduction, and a continuous 'beeeeeeeep' to indicate a short, or a very low depletion layer voltage. Handy.
Now that you know the basics of how a diode reads with a meter, you can test a transistor. The pic below shows simplified equivalent circuit of a NPN and a PNP transistor, as well as anode and cathode identification of a diode. Of course, you cannot 'build' a transistor like this, but it is a good visualization to help you understand how to check one.
Lets assume you have a transistor to test. Of course, this will require that you identify which lead is the base, collector, and emitter, and also determine if the transistor is an NPN or a PNP. Check the schematic, or the part number.
(hint: with Japanese transistors, all 2SAxxxx and 2SBxxxx transistors are PNP, and all 2SCxxxx and 2SDxxxx are NPN transistors. Often, the '2S' part of the transistor part number is omitted, thus a 2SA733 transistor is usually labeled 'A733', and the '2S' prefix is assumed)
Large TO-3 metal output transistors always have the outer case as the collector. Once you know that, you can figure out which of the other two pins are the base and emitter. Smaller transistors come in every configuration, EBC, BCE, ECB, so you need to either view the schematic to see which transistor leg connects to where, or find a data sheet for the transistor which will identify the leads for you. Of course, you can also figure it out for yourself.
Lets say you have found that you have a NPN transistor, and have identified the base, emitter, and collector. Set your meter for diode test, and place the positive lead on the base. Place the negative lead on the emitter. You should read a diode drop voltage of about 0.45 to 0.65V. Now place the negative lead on the collector. You again should read a diode drop of about 0.45 to 0.65V (these values are not written in stone...the 0.45 to 0.65V is the most common range however). Now place the negative lead on the base, and the positive on the emitter (called 'reverse biasing'). There should be no conduction. Now move the positive to the collector, and again, there should be no conduction. Lastly, move the negative to the emitter. Again, there should be nothing.
(note: most transistors fail with a dead-short from the emitter to the collector, especially in the later power stages of an amplifier. Knowing this can allow you to check high-power stages quickly for obvious failures)
For PNP transistors, the leads are reversed while doing the same checks as above (negative on the base to begin, positive on the emitter, and then on the collector etc. etc. to read the proper diode drops)
I must warn that when testing transistors in-circuit you are very likely to get voltage readings from collector to emitter, or when reverse-biasing the base-emitter or base-collector diode, all due to the multiple conduction paths in the circuit(s) that allow the meter current to flow around the component under test. Again, understand that most failed transistors short from collector to emitter, so if you read a voltage where you should not, that does not mean you have found a bad transistor. Yes, this complicates troubleshooting, but if this was easy, people would not be making a living fixing electronics. :scratch2: Bottom line...when in doubt, remove the transistor from the circuit and test it.
Last note...this type of test is generally worthless for finding transistors with 'leaky' junctions, as the voltage applied by a meter is very low and won't induce the failure. In a case like this, you will be reduced to measuring voltages with the circuit powered on to determine what is pulling excessive current, or just 'shotgunning' a whole section of the amp (replacing multiple components in the hopes of getting the bad one). Also, many old transistors will test just fine, but through age will have such low current gain that they can no longer do the job they were chosen for in the circuit. Relay driver transistors are especially bad about failures like this, where the transistor has spent hundreds of hours in a saturated state and gain eventually droops to the point that it can no longer close the relay. For this reason I replace relay driver transistors in amps as a matter of course, whether they are acting up or not.
Best of luck to ya!!