HOW TO CHECK A "MOSFET"

"MOSFET" stands for [Metal Oxide Semiconductor Field Effect TRansistor].  It is nothing but a transistor.  It is a semiconductor made of manufactured matereial that acts neither like a colductor or an insulator.MOSFET is a common type of transistor in which charge carriers, such as electrons flow along channels.  The conduction angle depends on the width of the channel. An insulation keeps current from flowing the Gate and the Channel.
See the structure and symbol used in schematics.

From the symbol you can see a MOSFET has three leads.  G=Gate, S=source & D=Drain.
There is a zener diode integrated in between source and Drain.  The most common failure to MOSFETs are by the shortage of this zener diode internally, which will show a very low resistance between source and Drain leads, in both direction.
How to check a MOSFET.
An Ohmmeter is connected between Drain and Source which should be very high, if the transisor has no leak between Source and Drain.  Connect an other Ohmmeter between Gate and Source. The Ohmmeter should be set to measure Megaohms. Now the test voltage comes from the meter [about 5VDC], when connected proper polarity, must turn the MOSFET 'ON". This ON possition will be indicated by the first Ohmmeter, which will measure low Ohm value.  It must show almost zero Ohms resistance.  To turn the transistor OFF, you have to reverse the Gate-Source voltage.  The Ohm-meter connected to Drain-Source must now measure very high resistance.
This is the common check procedure, and it is very like testing an oridinary transistor.  See some physical sturcture of MOSFETs.

There are mainly tow types  P-Channel MOSFET and N-Channel MOSFET.  We can determine the type used by the schematic diagram.  See the two types of them as schematic symbol.