The trial is only a demo version of the final product, from what i remember it doesnt require activation? It should just be a limited version of the full product, I'm not sure though, its been so long since i used the trial.
if you have you purchasde zbrush, I'm not too sure as your post isnt all that clear to me, you should have been provided with a product key when they emailed you the download link, if not, contact the company that handles pixologics orders (cant remember their name) they are useless, it took them easilly four months to send me my disc version of zbrush. just contact pixologic and they should put you in touch with that company.
How activation in zbrush works is you enter your product key (web activation is the best option, its all automated) then you should recieve an activation code, not by email, but it should be displayed on the webpage, you copy and paste that code into a dialog box that gets displayed in zbrush once you choose an activation method.
all of that applies to you if you've purchased the product, if not then either purchase it or if you want a free alternative go with what the others here have listed, sculptris is a good alternative, however if you are a student that you can also download mudbox for free using the same student method mentioned by mike5454,
Hope something in that essay of text helped
