You would use a digital multimeter (DMM for short) as you would analog multimeter.
First, you need to decide what electrical property that you wish to measure. Mainly, they are voltage, current, and resistance. Some high-end DMMs also allows you to measure capacitance and inductance.
Once you have figured out what you want to measure, you would then need to decide the range of your measurement. For example, if it is voltage that you want to measure, you want to make sure that your DMM is capable to measuring in the range of voltage that you are measuring. In measuring voltages, there is AC and DC voltage source - equally important to distinguish what type of power source you are measuring.
When you are measuring resistance, it is very important that you make sure the power to the circuit or the resistive element is turned off, otherwise you may cause damage to the DMM. Remember, when measuring resistance, the DMM actually supply a voltage to the resistive element, therefore, in effect measuring the current going through the resistive element.
When measuring the current, it is very important that you chose the right range of current that you would expect in the circuit, and adjust the DMM dial to that current range accordingly.
High end DMMs (Such as Fluke) has auto-range function for all of these 3 measurement functions, so you really do not need to worry about measurements going out of the range.
