Hey @MrSoftware, mine can output 0-5. It has a dedicated 5v and a dedicated 3.3v pin. All digital pins can output between 0-5v. It's the Arduino Uno Rev3. See my last post...given my attemps have failed so far, my next goal is to see if i can use a signal genrator for PWM (found some on amazon and ebay that are small enough and can generate the signal i need). But i'll have to be able to switch the source of the light to be either the signal coming from the PWM generator or straight from power supply + (when I don't want PWM). I'm not sure if that is possible.
At first glance, the spec says "Very Low RDS(on) at 4.5V VGS", which tells me the gate needs at least 4.5v to be considered fully-on. Some arduinos are 3.3v output and some 5v, are you sure yours is 5V?
Voltage is relative, so your scope ground must be connected to what you consider to be 0V for your circuit, such as - on your power supply. Else your readings will be meaningless. Put the probe on the drain of your mosfet. You're looking for the voltage at the drain to be 12v when the mosfet is off, and near 0v when the mosfet is fully on. If you see almost 0V when the mosfet is on, then that means it's fully on and working properly. You can put your second probe (other scope channel) on the mosfet gate to see both signals at once.
While in some cases it may be possible to connect the ground clip and probe across the load to measure voltage across the load, you have to be very careful about where you attach the scope ground clip. If your power supply is not isolated from the oscilloscope ground (wall outlet) then clipping the ground clip to a non-0V location would cause a direct short to ground through your oscilloscope ground, which rarely ends well.
Edit --> To answer your Vgth question; the threshold voltage is the gate voltage where it just begins to conduct, usually specified when there is a very tiny current through the mosfet. It does not tell you where the fet is fully-on.