If you don't want to characterize the device, but instead just test it (simple pass/fail) you can use a DMM. For a P-channel FET simply tie the gate to the source. Check continuity in both directions (drain->source and source->drain). Make sure there is no continuity, in other words the device is off.
Further check the cut-off and turn-off ability of the FET by attaching a resistor (RL) between a voltage source (say 10V) and the drain. Then attach the FET source lead to one end of your DMM (in current measuring mode) and the other end of the DMM to ground.
Connect the gate to ground and no current should flow. Connect the gate to the supply voltage (10V in this case) and current should flow.
You can to some degree but you can never really tell if its leaky or not Especially in Power Mosfets you need a decent Mosfet testing rig to achieve this
Just your finger touching the gate of a MOSFET can send it into full saturation In high frequency circuits and switch mode power supplies in some cases you cant even take measurements on these devices because the DVM probe is sufficient to blow the device up and your circuit
Yes, that is absolutely true. If the device is out of the circuit (which I was assuming for the answer above) you can attach a 1M "bleeder" resistor between the gate/source to make sure no charge builds up on the device's gate.
To test an N-channel MOSFET with a DMM and a 9 volt battery:
Tie the MOSFET gate to the source. Set the DMM to "diode" test mode and connect the DMM positive lead to the drain and the negative lead to the source. It should read infinite resistance. Reverse the DMM leads and it should read about 0.7 volts - the voltage drop across the MOSFET intrinsic source-to-drain diode. In this test the MOSFET is biased OFF.
Now connect the 9 volt battery between the gate and the source; positive to the gate and negative to the source. Set the DMM to "resistance" mode and connect the DMM leads to the source and drain. It should read the MOSFET ON resistance.