Large resistors usually have the maximum watt rating printed on the resistor, but many times smaller resistors do not indicate this. Common sizes are .25W, .5W, 1W, 2W, and 5W. The higher the wattage, the larger the resistor will be. Over time you could probably guess the watt rating of these smaller resistors by looking at them. When replacing a bad resistor a good rule of thumb is to replace it with a resistor of at least the same or larger physical size.
Watts can be calculated by multiplying Voltage by Current (V*I=W). So if you are constructing a circuit that is 5 Volts and a maximum of 0.15 Amps, you will need a resistor that is at least 0.75 Watts (V*I=W –> 5Volts * 0.15Amps = 0.75Watts). You would use a 1 Watt resistor in this situation since it is the next larger common size.