Depending on how often you'll be doing an update, you could simply have a page on your server that gives you the latest version available, and if it doesn't match the current one, prompt the user with an intent that opens the play store at your app.
Basically, ask the server what the latest version is (you'll need to wrap this in a try/catch and add the internet permission to the manifest):
URL url = new URL("mysite.com/thefile.txt");
BufferedReader in = new BufferedReader(new InputStreamReader(url.openStream()));
String str;
while ((str = in.readLine()) != null) {
// str is one line of text; readLine() strips the newline character(s)
}
in.close();
The response from the server could be something like {"latestVersion": "1.004"}
and you can check the current installed version with:
PackageInfo pInfo = getPackageManager().getPackageInfo(getPackageName(), 0);
version = pInfo.versionName;
Compare them, and prompt the user with a dialog or whatever and then launch the play store, by using the code found here:
final String appPackageName = getPackageName(); // getPackageName() from Context or Activity object
try {
startActivity(new Intent(Intent.ACTION_VIEW, Uri.parse("market://details?id=" + appPackageName)));
} catch (android.content.ActivityNotFoundException anfe) {
startActivity(new Intent(Intent.ACTION_VIEW, Uri.parse("http://play.google.com/store/apps/details?id=" + appPackageName)));
}
To clarify, you'll be updating the version in your server manually so that may or may not be an option for you depending on the frequency of your updates, and how often you forget things :P