public class SplashScreen extends Activity implements Runnable {

    @Override
    public void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.splash);

        Handler handler = new Handler();
         // define o tempo de execução em 3 segundos
        handler.postDelayed(this, 3000);
    }

    public void run(){
        // inicia outra activity após o termino do tempo
        startActivity(new Intent(this, ActivityMain.class));
        finish();
    }
}

<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
    android:orientation="vertical"
    android:layout_width="fill_parent"
    android:layout_height="fill_parent">

    <ImageView
        android:layout_width="wrap_content"
        android:layout_height="fill_parent"
        android:layout_gravity="center"
        android:src="@drawable/imagem"/>

</LinearLayout>

<application android:icon="@drawable/ic_laucher" android:label="@string/app_name" android:debuggable="true">

  <activity android:name="SplashScreen" android:label="@string/app_name">
    <intent-filter>
       <action android:name="android.intent.action.MAIN" />
       <category android:name="android.intent.category.LAUNCHER" />
    </intent-filter>
  </activity>

  <activity android:name="ActivityMain" android:label="@string/app_name">
    <intent-filter>
       <action android:name="android.intent.action.MAIN" />
    </intent-filter>
  </activity>
</application>