The main constraint on the mosfet switching time is charging and discharging the gate. The mosfet datasheet usually gives a figure for total gate charge. This value varies with the drain voltage you are switching (the higher the voltage, the higher the total gate charge). To estimate the switching time, use the figure on the datasheet. The time taken to switch the gate is the total gate charge divided by gate drive current. The gate drive current is the excess gate drive voltage divided by the series resistor. The excess gate drive voltage depends on the mosfet and the driving voltage, but for a rough estimate you could assume one third of the gate drive voltage.
Example: 5V Arduino driving a STP40NF10L (total gate charge 46nC typical, when switching 80V @ 40A) through a 220 ohm series resistor:
t = 46nC * 220ohms / (5V / 3) = 6072ns
So you can see that for fast switching, you need to drive the gate from a low resistance source, which is what mosfet driver chips are for.