mDatabaseHelper = new DataBaseHelper(this, "mydatabase.db", null, 1);
mSqLiteDatabase = mDatabaseHelper.getWritableDatabase();

Cursor cursor = mSqLiteDatabase.query(DataBaseHelper.DATABASE_TABLE, new String[]{
        DataBaseHelper.NAME,
        DataBaseHelper.NUMBER},
        null,null,null,null,null);

Process: ru.startandroid.begin, PID: 12643
    java.lang.RuntimeException: Unable to start activity ComponentInfo{ru.startandroid.begin/ru.startandroid.begin.StartActivity}: android.database.sqlite.SQLiteException: no such table: database1 (code 1): , while compiling: SELECT name, number FROM database1
    #################################################################
    Error Code : 1 (SQLITE_ERROR)
    Caused By : SQL(query) error or missing database.
    (no such table: database1 (code 1): , while compiling: SELECT name, number FROM database1)
    #################################################################
    at android.app.ActivityThread.performLaunchActivity(ActivityThread.java:3184)
    at android.app.ActivityThread.handleLaunchActivity(ActivityThread.java:3294)
    at android.app.ActivityThread.access$1000(ActivityThread.java:210)
    at android.app.ActivityThread$H.handleMessage(ActivityThread.java:1704)
    at android.os.Handler.dispatchMessage(Handler.java:102)
    at android.os.Looper.loop(Looper.java:145)
    at android.app.ActivityThread.main(ActivityThread.java:6938)
    at java.lang.reflect.Method.invoke(Native Method)
    at java.lang.reflect.Method.invoke(Method.java:372)
    at com.android.internal.os.ZygoteInit$MethodAndArgsCaller.run(ZygoteInit.java:1404)
    at com.android.internal.os.ZygoteInit.main(ZygoteInit.java:1199)
    Caused by: android.database.sqlite.SQLiteException: no such table: database1 (code 1): , while compiling: SELECT name, number FROM database1
    #################################################################
    Error Code : 1 (SQLITE_ERROR)
    Caused By : SQL(query) error or missing database.
    (no such table: database1 (code 1): , while compiling: SELECT name, number FROM database1)
    #################################################################
    at android.database.sqlite.SQLiteConnection.nativePrepareStatement(Native Method)
    at android.database.sqlite.SQLiteConnection.acquirePreparedStatement(SQLiteConnection.java:1093)
    at android.database.sqlite.SQLiteConnection.prepare(SQLiteConnection.java:670)
    at android.database.sqlite.SQLiteSession.prepare(SQLiteSession.java:588)
    at android.database.sqlite.SQLiteProgram.<init>(SQLiteProgram.java:59)
    at android.database.sqlite.SQLiteQuery.<init>(SQLiteQuery.java:37)
    at android.database.sqlite.SQLiteDirectCursorDriver.query(SQLiteDirectCursorDriver.java:44)
    at android.database.sqlite.SQLiteDatabase.rawQueryWithFactory(SQLiteDatabase.java:1454)
    at android.database.sqlite.SQLiteDatabase.queryWithFactory(SQLiteDatabase.java:1301)
    at android.database.sqlite.SQLiteDatabase.query(SQLiteDatabase.java:1172)
    at android.database.sqlite.SQLiteDatabase.query(SQLiteDatabase.java:1340)
    at ru.startandroid.begin.StartActivity.onCreate(StartActivity.java:30)
    at android.app.Activity.performCreate(Activity.java:6575)
    at android.app.Instrumentation.callActivityOnCreate(Instrumentation.java:1134)
    at android.app.ActivityThread.performLaunchActivity(ActivityThread.java:3137)
    ... 10 more

package ru.startandroid.begin;

import android.content.Context;
import android.database.DatabaseErrorHandler;
import android.database.sqlite.SQLiteDatabase;
import android.database.sqlite.SQLiteOpenHelper;

public class DataBaseHelper extends SQLiteOpenHelper {
    // имя базы данных
    private static final String DATABASE_NAME = "mydatabase.db";
    // версия базы данных
    private static final int DATABASE_VERSION = 1;
    //имя таблицы
    public static final String DATABASE_TABLE = "database1";
    // название столбцов
    public static final String NAME = "name";
    public static final String NUMBER = "number";
    //скрипт создания
    private static final String SCRIPT = "CREATE TABLE IF NOT EXISTS "
        + DATABASE_TABLE + " ("
        + " integer primary key autoincrement, " + NAME + " text no null, "
        + NUMBER + " long, " + " (Field1 VARCHAR, Field2 VARCHAR;)";

    DataBaseHelper(Context context) {
        super(context, DATABASE_NAME, null, DATABASE_VERSION);
    }

    ////конструктор БД
    public DataBaseHelper(Context context, String name,
                            SQLiteDatabase.CursorFactory factory, int version) {
        super(context, name, factory, version);
    }

    public DataBaseHelper(Context context, String name,
                            SQLiteDatabase.CursorFactory factory, int version,
                            DatabaseErrorHandler errorHandler) {
        super(context, name, factory, version, errorHandler);
    }


    @Override
    public void onCreate(SQLiteDatabase db) {
        db.execSQL(SCRIPT);
    }

    @Override
    public void onUpgrade(SQLiteDatabase db, int oldVersion, int newVersion) {
        // Удаляем старую таблицу и создаём новую
        db.execSQL("DROP TABLE IF IT EXISTS " + DATABASE_TABLE);
        // Создаём новую таблицу
        onCreate(db);
    }
}

package ru.startandroid.begin;

import android.app.ListFragment;
import android.app.ListActivity;
import android.content.Intent;
import android.database.Cursor;
import android.database.sqlite.SQLiteDatabase;
import android.os.Bundle;
import android.util.StringBuilderPrinter;
import android.view.View;
import android.widget.ArrayAdapter;
import android.widget.ListView;

public class StartActivity extends ListActivity {
    private ArrayAdapter<String> mAdapter;
    private DataBaseHelper mDatabaseHelper;
    private SQLiteDatabase mSqLiteDatabase;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);

        //подключаемся к БД!!!!!
        //mDatabaseHelper = new DataBaseHelper(this, "mydatabase.db", null, 1);
        //mSqLiteDatabase = mDatabaseHelper.getWritableDatabase();
        mSqLiteDatabase = this.openOrCreateDatabase("mydatabase.db", MODE_PRIVATE, null);

        ///////////////////////////////////// List
        Cursor cursor = mSqLiteDatabase.query(DataBaseHelper.DATABASE_TABLE, new String[] {
            DataBaseHelper.NAME,
            DataBaseHelper.NUMBER},
            null,null,null,null,null);
        //cursor.moveToFirst();
    }
}