To start with, make sure you are a frequent flyer, and you do fly frequently: after all, if Malaysia are going to upgrade anyone, they will upgrade those passengers who fly with them pretty regularly, and hence will enjoy the upgrade enough to put more business Malaysia's way. Then if the flight is full in economy, and someone needs to be moved up, the check in staff will first look at Enrich Gold members. Another thing that Malaysia look at is how much you paid for your ticket: it's much more likely to happen with a full fare ticket (although occasionally you can get lucky with a discounted economy ticket). On Malaysia the airline has heard - probably hundreds of times a day - requests for an upgrade: the general consensus seems to be that if you ask for an upgrade, you're more likely to get it, although opinions differ on an upgrade strategy for Malaysia Airlines.
As always, my advice on dressing properly in the pages on how to get an upgrade applies.
Information on their E-ticketing is also hidden away. If you book online you can't E-ticket for international flights to Thailand - instead you have to click the box which says collect them from the ticket office in central KL. It does however print out a summary.
There are some special fares hidden away, if you travel midweek and include a Saturday night, but these rise if you travel on a Friday or Saturday.
Note that some Thai airways flights are shown as fully booked on Thai's website, however you can book them as Malaysian, if they are a Thai codeshare on Malaysia metal.