How can I start with database programming in C++ or VC++ without MFC and without any third party library.

The most efficient way for doing so would be using SQLite3[^].
This is an open source project. The Windows version doesn't require any additional framework and you can use it with plain Win32 API.
SQLite3 lacks proper support for UNICODE, so I usually use a wrapper called CppSqlite3[^] which is also very simple and straight forward.

Here is an example I wrote:

// An example for updating a record: Update or Replace the value of FieldValue in field FieldName
bool UpdateRecord(bool UpdateOnly, CString FieldName,CString FieldValue)
{
	CppSQLite3DB temp;
	temp.open(DBName);


	CString sql;
	if (UpdateOnly)
	{
		sql = (CString)L"UPDATE log " + (CString)L" SET " + FieldName + L" = " + FieldValue;
	}
	else
	{
		sql = L"REPLACE INTO log (" + FieldName + L") VALUES ('" + FieldValue + L"')";
	}

	CppSQLite3Query SqlQuery;
	try
	{
		SqlQuery = temp.execQuery(sql);
	}
	catch (CppSQLite3Exception & e)
	{
		temp.close();
		return false;
	}
	temp.close();
	return true;
}