Undoubtedly the most complete online course for learning Malay - and it's completely free! This is the smartphone version. The full version, which discusses the Indonesian language as well, can be found here. 

Basic Malay Language Course  Table of Contents

Hi everyone,
You can now learn Malay wherever you are (at the bus-stop, in the subway or even while waiting in a queue) with just your 3" smartphone or 7" tablet.
In fact the above course of 64 lessons has been redesigned so that whether you are using a smartphone, tablet, netbook, laptop or desktop the pages will adapt themselves to the width of your device. Hope this will make your learning of the Malay language more comfortable and convenient.
I wish to emphasize that this is just a basic course and is meant for beginners only. Advanced students of Malay are kindly requested to look elsewhere.

As this is a basic course I am assuming, of course, that your aim in studying the Malaysian language from here is to be able to understand and to make yourself understood when you travel to Malaysia. If your study is of an academic nature then of course you will have to go through a proper school and attend regular classes and do practical exercises to gain proficiency.

Let's get started!