How do I drive a MOSFET when I have an 11.1v power-supply and an arduino
Really simple -- get an ESC that's compatible with the motor.  I don't know if an "airsoft motor" is a DC brushed motor or a DC brushless -- count the leads.  If it's got two, then you need an ESC for a brushed motor; if it's got three, then you need an ESC for a brushless motor.  All you need then is a servo output from the Arduino, and that's built into their code base.
Complicated-er (for your) and less capable: switch the MOSFET gate voltage with a transistor.  Note that, as drawn, the signal from the Arduino means "off", so the motor will go on with battery power until the Arduino comes up.  You'll need another 2N3904 stage for the thing to be off when there's no Arduino.








simulate this circuit &ndash; Schematic created using CircuitLab