Hi there,
You can explore it's forward voltage drop by running it with a known current
and measuring the voltage across the diode. You can do this for several
currents from 100ua to 10ma and see if the diode gets hot. If not, keep
going. You can then plot a curve.
You also need to check it's reverse characteristics.
You can estimate it's power by noting how hot it gets.
The only way to check it's reverse voltage is to use a voltage supply
(might have to go up to several hundred volts) and check the leakage
current as you increase voltage. Compare with other diodes of known
types and voltage ratings.
In general however it's best to buy a diode so you know for sure
what the characteristics are.
Use that unknown diode for something not too important.