I downloaded the trial version of Office professional plus 2013 in January - I couldn't install it as I didn't have a disc drive on my laptop.  I have now set it up on another laptop but I cant activate it - it is stating that the office product is not associated with my Microsoft account. I have 2 days to activate it. How do you activate this trial version? Please give me an simple answer - I am a basic computer user!

Follow the standard process to install Office 2013 pro plus trail version, you will download the installation and product key for trial version, right?
Whats going on when you install it in your first machine?
After you install Office 2013 in second machine, have you typed the correct product key under the proper Microsoft account?
In any Office product, try to switch Microsoft account in File > Account and type the product key youve got.

If you still failed to activate Office, please re-apply the product key from the link below:
http://technet.microsoft.com/en-in/evalcenter/jj192782.aspx

The following thread may also help you:
http://answers.microsoft.com/en-us/office/forum/office_2013_release-office_install/microsoft-office-2013-trial-activation/de022ca3-a719-40f1-85f9-d6d60efe730a  

Tony Chen
TechNet Community Support