The easiest way to tell the difference is to look into the air vents of your drill with the motor engaged. If you see sparks, then the likelihood is you have a brushed variety.
The other way to tell is to get a feel for the drill when you use it. It will adjust the torque automatically depending on the task it is used for. Also, brushless motors make less noise, so if you think your drill is quieter, you probably have a brushless motor.
The third way to tell is to look at the size and weight of the drill. Brushless motors are smaller and more compact, making them lighter and more nimble to use.