Adjusting to a new phone--even learning how to receive a call--can take some time, especially if you're going from a regular cell phone to a smartphone such as the Droid. There are many different Droid models, but they are all based on the Android operating system, so most Droids have the same basic functionality.
Press the "Power" button on top of the Droid to see whether the phone is off or on. A Droid appears the same whether it is turned off or whether the screen is just off to save battery power, but you must turn the phone on to receive calls. If the screen is off, the screen will turn on once you press the button. If the phone is off, hold the power button until the phone turns on.
Look at who's calling. When someone calls your phone, your screen will turn on and the number of the person calling will appear. If the person is in your contacts, his name will appear instead of a number.
Touch the green "Phone" icon and slide the icon to the right to answer the call. Hold the phone up to your ear so that the top part of the front screen is facing your ear. Begin talking.