How to measure ratings of a transformer?
You need to know some basic specs for the transformer before you can start.  In particular, you need to have some idea of the intended frequency if it is a power transformer.

I would start by measuring the DC resistance of all the windings.  If you are given a transformer with many leads and no other information, these DC resistance measurements will also tell you which leads belong to each winding.

Start with the winding that has the highest DC resistance.  Feed in a low-voltage signal at the frequency that the transformer is designed to operate at.  Measure the voltage out of all of the other windings - you want to get an idea of the turns ratio of each winding.

Now it becomes a tiny bit more complicated.  But not much.

You want to increase the signal amplitude into that winding to find out where the core begins to saturate.  How you do this depends on the transformer, whether it is designed for AC Mains operation (50 / 60 Hz) or some other frequency.

If the transformer is designed to operate from the AC Mains, connect a small (60 Watt) light bulb in series with a Variac and drive the winding.  Either monitor the AC waveform using an oscilloscope or simply increase the input AC voltage until the bulb brigtness begins to increase significantly.  The onset of saturation is usually quite well defined.

That tells you the maximum voltage that this winding can tolerate.

Got to go - will return.