OK, basically a multimeter is a device for measuring a multitude of electrical and electronic things. For example, a multimeter usually includes a voltmeter (for measuring voltage, or potential difference as it is sometimes called), an ammeter (for measuring amps, which is electrical current), and an ohmmeter (not sure of the name or the spelling, but this measures electrical resistance). Some also can measure things to do with transistors, and both AC (alternating current, like the mains) and DC (direct current, like what a battery produces).
To use the device, usually you set it to whatever quantity you want to measure, for example volts, amps, or ohms, and select a sensitivity higher than what you expect to be measuring. So if you want to measure what you think might be a 12 V batter, you set it to whatever voltage is above 12 V. It might go up from 2 V, to 20 V, to 200 V, and in this case you set it to 20 V. (Always set it to higher to avoid causing damage to the multimeter.) You can then touch the two leads accross the battery and the display should show you the voltage. Depending on the meter, you may have to be careful to touch the leads the right way round, red to positive, black to negative.
As for it being digital, there is no difference in operation between an old style analogue meter and a digital one.