It's been a looong time since I did consumer electronics repair for
tuition, but I used to use the hell out of a Radio Shack transistor
tester. Had several transistor sockets for the small-signal types and
three leads with clips for the big stuff. The way it worked was that
there was the makings of a simple audio oscillator on-board, minus the
transistor. The oscillator fed a garden-variety audio output
transformer which was connected to a neon light on the front panel.
Good ones lit the bulb, bad ones didn't. You could get a rough idea
of how good the amplifying parameters of the particular part were by
turning a pot. The farther around the pot went before the light went
out, the better the transistor was. Still have it somewhere, worked
off a C-cell, usually a Battery-of-the-Month in my case. All the
parts inside and out used to hang on the pegs at the stores, Radio
Shack ate their own dogfood on this one. Don't know if it's still
available. Was pretty cheap at the time. Strictly an out-of-circuit
tester.
Static testing on transistors is usually iffy. You can get leaky ones
that may look good with an ohmmeter, but don't work. You can also
blow the really sensitive types using an old-style analog meter.
Some circuits require matched transistors, usually not consumer
equipment, matching is expensive. Only gizmo I know of that would do
curve matching was a very expensive Tektronix dual curve tracer, multi
K-bucks. Derived from one of their high-end scopes. Usually circuit
design parameters are such that transistors can vary 20-50% on
internal parameters and the circuit would still work. That's the way
the "universal" replacement part biz got started.
As far as how-to, the other poster got it right. Power supply first,
preferably with an O-scope to see if the filter caps are open, leaky
or shorted, followed by voltage checks around the circuit to see if
everything is getting supplied correctly. Then you hook up a signal
source and start tracing. They used to sell an audio signal tracer
for the guys in the radio repair biz that didn't have a scope, just
was a small isolated amp with a speaker and a probe. A circuit
diagram is a really good thing to have for this stuff, I've done
without, but a beginner is going to be lost. It takes a whole lot
longer, too.
Stan