You need to look at drain-source resistance vs. gate voltage. The datasheet covers it preety well. From there just calculate voltage drop and power. The gate voltage threshold is the minimum voltage that you need to apply to make the device show some action. It will not turn on fully though and have quite large R(DS) values and therefore get hot. To use it, you should apply more than 3V to the gate. Just look at the graph R(DS) vs. V(GS). The on-resistance of that transistor with over 1 Ohm is quite high, but if that is good or bad depends on how much current you need to switch.
Sorry I haven't replied sooner... I must have not had my "topic reply email notification" turned on... (aka, I just came back to check my original post this morning).
So, what I'm taking away from your responses (thanks, btw) is ...
... that the 3v max Vgs, is just the minimum that must be supplied to turn the transistor "full on"?
If I DON'T apply more than 3V to the gate, the thing will get hot...
R(DS) varies with V(GS)...
OK, now my follow up questions.
I'm planning to use this MOSFET with the TLC5940 current sinking PWM LED driver to drive higher voltage strings of LEDs...
Assuming I use 5V as the gate turn-on source, will I need to use a resistor in between the 5V and gate?
It's still not clear how I calculate the Vds for a given gate voltage supplied? I didn't see a graph of R(DS) vs. V(GS) in the data sheet as madworm mentioned... Is there a V(gs) vs. V(ds) graph? Or does the amount of I(ds) I allow factor into this equation...
Assuming I use 5V as the gate turn-on source, will I need to use a resistor in between the 5V and gate?
Yes but not for the reason you think. You need something like a 50R to limit the inrush current of the uncharged FET gate, It's nothing to do with the voltage.
It's still not clear how I calculate the Vds for a given gate voltage supplied?
Vds is the voltage between the drain and the source, it is not something you have to calculate it is something "that is" from the design of the schematic. Just make sure it is not greater than the limit in the FET data sheet.
TLC5940 current sinking PWM LED driver to drive higher voltage strings of LEDs.
Have you seen the app note slva259 that tells you about such things?