If you've patched to 1.03, under the "Versus" menu you should have the option available for either a Team battle or a Tag battle.
For playing against others online, you'll need to download the MBCaster netplay client, which you can find at Melty Bread
, and to find opponents you can use either Hamachi
. If you read through the thread at Melty Bread, you should be able to find more information on match-making.
EDIT: Come to think of it, I remember being frustrated by the fact that when I started playing there was no in-depth, informative tutorial on exactly how to get netplay working. I'm going to do a walkthrough of the whole process; look for it in the next few days.