A transistor is a "3-legged" device. Using an ohm meter, you can check for "gross" failures. From the base to emitter you should see a diode (relatively low resistance with the meter's leads connected one direction, very high resistance with the meter's leads flipped). Same with the base to collector junction. Collector to emitter should be high R with test leads in either configuration. Experiment with a "known good" transistor to get the "feel" of how your meter responds. Also keep in mind that "in circuit" tests like these may yield bogus results.
To "ohm" a given resistor, set your meter on the "ohms" scale and read the resistance, then compare it to the value marked on the part or in the schematic. Again, "in circuit" numbers may be waaay off the mark.
"Shotgun" means to replace any/all suspect parts.
Testing caps requires that your metering gear can read capacitance values, and again, you might come up with bogus values while testing the parts in-circuit.
Bri