Not entirely true.
While anyone can download the game client for free, and even usually get 10-14 days play free (up to level 20, where it stops gaining exp for any chars at level 20), before you can then subscribe to WOW, you have to then buy WOW as well as your subscription.
It only comes down to about an extra $15 bucks though as WOW also comes with another 30-days when you buy it for around $29, which includes a $14.99 free month with the purchase price.
So in a nutshell, if you're on any one of the various WOW freebie versions, at the end of the trial you'll need to:
a) Pay the $29 for WOW, which includes another month/30 days.
b) Pay another $39 if you wish to add the Burning Crusade expansion (Blood Elves and Draeni races if you roll these).
c) Continue to pay up to $14.99 a month after the second month to keep your subscription current (whether it be WOW or WOW + Burning Crusade expansion.. Monthly fee is the same). By "up to", this means if you make a 3-month or 6-month recurring subscription, you can save a few bucks for paying for more months.
You wont have to download or install anything else, except maybe the expansion pack. The "trial" client is the full client, but you have to "pay for it" should you decide to keep playing.
Hope this helps!