I want the Android phone, should I buy a Motorola Droid?
Droid and Android are very similar sounding names, but they are not the same thing. The Motorola Droid line of phones are a make and model name of particular devices. Android is a mobile operating system used in many different makes and model of smartphone. Google built the Android system, and smartphone manufactures like Motorola then use the system to run their mobile devices. To answer the question, yes, the Droid phones all run Android, but you can buy many other devices not named 'Droid' and still get the Android system.
What is the Ice Cream Sandwich?
This is also a bit confusing, but the Android system, like many pieces of software, is imperfect and therefore must be periodically updated to fix minor problems or upgrade new features. In many software ecosystems, new versions are given a 2.0 indicator when they are updated. Android 2.0 preceded Android 3.0 and is now going to be updated this year by Android 4.0. Each of these versions is given a nickname by Google, and each successive version has a new name, in alphabetical order, of a sweet treat like ice cream. There was Donut, Eclair, Froyo, Gingerbread and now Ice Cream Sandwich. (not a complete list of version names) Ice Cream Sandwich is the newest version, known as Android 4.0, and it will launch when the Samsung Galaxy Nexus smartphone debuts in November.
Does Sprint have Android, or do I have to use Verizon?
Yes, many Android versions will run on either Sprint or Verizon, but the carrier and operating system are not really related in that way. The carriers only determine what type of broadband network the device will run on, not what type of operating system it uses (Of course, they also often determine pricing; a whole other FAQ). Because Android is an operating system, the device it powers can run on any carrier network as long as it can communicate with the carriers' signal antennas.
I want the (insert name of wildly popular app). Will that app work on Android?
Many app developers are building versions of their apps for the Apple App Store and for the Android Market. To download apps to your Android device, go to the Android Market. Sometimes an app will debut in the App Store, and then the company that made it will develop an Android version, and vice versa.