According to an article at macgasm, Apple is working hard to make sure everybody that wants to transition from mobile me to iCloud has the ability to do so before June 30th when the mobile me service will officially shut down.
Apparently if you are still a mobile me user, you can login to your account here and request the free DVD of Snow Leopard. At that point you will have access to the App Store and can purchase Lion for $29 (which is required for using the iCloud service on your computer).
Of course, if you are keeping alive some very old hardware running Leopard, you may also want to check the minimum hardware required for Lion before you get your hopes up about switching to iCloud. Of course, even if you can't upgrade to Lion, you may still want to get the free DVD of Snow Leopard.
Click here to see the minimu specs for Lion.