To check whether a resistor is good or not, we only need to  check the resistor's resistance value by using the ohmmeter of a multimeter. This is the best, easiest and most effective way .

Take the ohmmeter and place its probes across the leads of the resistor and do not pay much attentio to the orientation as resistance isn't polarized. 

The resistance showing in the  ohmmeter  should be close to the rated resistance of the resistor. For example, when the resistance value of a resistors is 100Ω resistor with a tolerance rating of 1%. Therefore, the resistance of the resistor can vary between 99Ω and 101Ω.

If the value  reading in the ohmmeter is within the tolerance range of the resistor, the resistor is good. Otherwise, it is defective and need to be replaced.

How to judge whether it is shorted or open

If a resistor is reading a very low resistance, near 0Ω, it's shorted internally. Then it is defective and should be replaced.

If a resistor is reading a very high resistance and above its rated value, it is open. It is defective and need to be replaced.