Currently most developers accomplish this using one of the following 3 techniques.
The first approach is easily circumvented, the first time you run the app save the date/time to a file, database, or shared preferences and every time you run the app after that check to see if the trial period has ended. This is easy to circumvent because uninstalling and reinstalling will allow the user to have another trial period.
The second approach is harder to circumvent, but still circumventable. Use a hard coded time bomb. Basically with this approach you will be hard code an end date for the trial, and all users that download and use the app will stop being able to use the app at the same time. I have used this approach because it is easy to implement and for the most part I just didn’t feel like going through the trouble of the third technique. Users can circumvent this by manually changing the date on their phone, but most users won’t go through the trouble to do such a thing.
The third technique is the only way that I have heard about to truly be able to accomplish what you want to do. You will have to set up a server, and then whenever your application is started your app sends the phones unique identifier to the server. If the server does not have an entry for that phone id then it makes a new one and notes the time. If the server does have an entry for the phone id then it does a simple check to see if the trial period has expired. It then communicates the results of the trial expiration check back to your application. This approach should not be circumventable, but does require setting up a webserver and such.
It is always good practice to do these checks in the onCreate. If the expiration has ended popup an AlertDialog with a market link to the full version of the app. Only include an “OK” button, and once the user clicks on “OK” make a call to “finish()” to end the activity.