Suppose you have made a reservation with Malaysia Airlines and selected the premium economy to travel. Still, since then, you have not been able to get the appropriate flight, get the best services, and access the best facilities to travel to your desired destination. You should go with the upgraded travel class because you will pick the best class and seat to travel. However, if you seek essential information for a Malaysia Airlines business class upgrade, in that case, you need to use the following passage because it will help you get the upgrade processed consistently.

Visit Malaysia Airlines' official website and select the login tab
Now, enter the required information, which will enable you to access the account 
Furthermore, you get to choose the My Trips icon and enter the booking reference number and last name of the passenger
Next, proceed with the selection of the ticket and tap the upgrade button 
Once you upgrade, select the next travel class, seat, and other amenities. 
Proceeding with it, you select the new travel ticket available for your new travel. 
Ultimately, the charges to upgrade are made by upgrading the ticket. 

How do I get a complimentary upgrade to business class?

Since you were looking to get a complimentary upgrade to business class, you must have a few basic points for it, and the listed points are mentioned in the section below. 

Loyalty Programs 
Using mileage points
Understand well about Malaysia Airlines' upgrade policies.
 
Is upgrading to business class cheaper at the airport?

Generally, if you are planning to upgrade to a business class but want to select this option at the airport, then you may or may not get the option of doing so quite easily because the airline upgrades for the new class at airport is possible only if there are vacant seats available.