sqliteDatabaseクラスをインポートするので、実際にすでに利用可能なものを拡張する必要はありません。
簡単な定義:
Sqlitedatabase dbname;
dbname.execSQL(Query);
または:
public class MySQLiteHelper extends SQLiteOpenHelper {
  public static final String TABLE_COMMENTS = "comments";
  public static final String COLUMN_ID = "_id";
  public static final String COLUMN_COMMENT = "comment";
  private static final String DATABASE_NAME = "commments.db";
  private static final int DATABASE_VERSION = 1;
  // Database creation sql statement
  private static final String DATABASE_CREATE = "create table "
      + TABLE_COMMENTS + "(" + COLUMN_ID
      + " integer primary key autoincrement, " + COLUMN_COMMENT
      + " text not null);";
  public MySQLiteHelper(Context context) {
    super(context, DATABASE_NAME, null, DATABASE_VERSION);
  }
  @Override
  public void onCreate(SQLiteDatabase database) {
    database.execSQL(DATABASE_CREATE);
  }
  @Override
  public void onUpgrade(SQLiteDatabase db, int oldVersion, int newVersion) {
    Log.w(MySQLiteHelper.class.getName(),
        "Upgrading database from version " + oldVersion + " to "
            + newVersion + ", which will destroy all old data");
    db.execSQL("DROP TABLE IF EXISTS " + TABLE_COMMENTS);
    onCreate(db);
  }
}