From the datasheet:
Static Drain-Source On-Resistance RDS (ON): 42 m? max @ VGS = 4.5V, ID = 4.8A
So that mosfet is suitable for driving from an Arduino (because the Rds(on) is specified at 5V or less), but you shouldn't switch more than 4.8A with it (because the effective Rds(on) may increase dramatically above that current).
The other important parameters are Vds(max) which must be higher than the voltage you want to switch, and Pd(max) which (in conjunction with Rds(on)) also limits the continuous current you can switch.
zenwebb:
Is a series resistor required (or good practice) on the gate?
It's good practice, especially if you are using PWM. 100 ohms is a suitable value.