Well, if it is entirely out of the circuit, the easiest thing you can check is the input windings and the output windings. A transformer is two coils of wire, insulated from each other, wrapped around a (typically) iron core. The exact shape of the core and how the wires are wrapped will vary, but all are the same. The input windings current causes voltage to be induced in the output windings as the magnetic fields change with the a/c signal. The ratio of input to output depends on the amount of loops relative to the input vs output. So, you can make the output voltage higher or lower depending on which side has more windings. The amount of current it can handle is dependent on the size of the wire, the amount of windings, the core, and heat disipation capacity.
With an ohmmeter, the input windings should show continuity from one lead to the other. The output windings should show continuity between them. There should not be any continuity from the input windings to the output windings. Now, exactly what those readings will be will depend on the current capacity and whether it is a step-up or step-down transformer. If it is more than say 20-30 ohms, (usually much less but depends on the design) there may be a problem.
Typically, a transformer is pretty stable item. If it doesn't smell from having been overheated, and it has continuity in the windings, it is probably okay.
Note, this only applies to a real transformer...some, for low-voltage supplies use an electronic equivalent which has active circuitry in it...this simple test won't work.