Google Play, formerly known as the Android Market, is the digital application distribution platform for Android apps. In order to publish an app on Google Play, you have to log in with your Google account and follow the steps outlined at https://play.google.com/apps/publish. When registering, remember to have a credit card available because you will be required to pay a fee using Google Wallet before adding the developer details (that is, name, telephone number, e-mail, and so on).
Once you complete the registration process, you can add your apps to the developer console. For each app, you can define the countries in which you want to distribute it, the carriers you want to target, specify whether it's a free app (if you want to sell an app you have to provide a valid Google Wallet merchant account), set up an alpha and beta group for testing and the staged rollouts, and so on. In order to get new users to download and install the app, it's very important to provide detailed information, icons, screenshots, and so on. The Android online guide available here https://support.google.com/googleplay/androiddeveloper/answer/1078870 is the place to start in order to get a better understanding of the required graphic assets.
In addition, your app has to be less than 50 MB in size and signed using the keystore tool as described at http://developer.android.com/tools/publishing/app-signing.html. For apps that require more than 50 MB see the APK expansion details at http://developer.android.com/google/play/expansion-files.html.