The most important specifications of a diode are:
- maximum forward current
- peak inverse voltage (aka maximum reverse voltage)
- reverse leakage current
- reverse turnoff time (very important in high speed switching diodes)
- maximum power dissipation (only given for power rectifier diodes)
- forward bias knee voltage
- parasitic capacitance (only important in high frequency applications)
All of this and more can be found in the datasheet for the diode.