ATtiny85 to control a relay, which will turn on and off a motor
You should not really drive the relay coil directly from the microcontroller pin. 

Instead, I would recommend using an NPN transistor between GND (emitter) and the coil (collector), then connect the other side of the coil to the positive supply directly. 

Connect a diode backwards in parallel to the coil (i.e. diode cathode to positive supply, diode anode to transistor collector). This is a "fly-back" diode to protect against the back-EMF you get with the coil switches.

Put something like a 330 ohm resistor in series between the transistor base and the microcontroller pin. This limits the current into the base of the transistor to a level that is within the capabilities of the microcontroller.

That's the most common way I know of to control a relay with a GPIO pin of a micrcontroller.