Props to talismanisland for pointing this out:
How to find PM's
Go to your profile, click to see your list of friends and there is a PM icon next to them.
..and as an aside, The column to the left of the PM icon shows a birthday cake when it is one of your friends has a birthday!
Again, thanks to Talismanisland for point that out.
After using it, it turns out that it sends an email. You also get the following message:
The message has been sent correctly. Please take into account that this message was sent through Fantasy Flight and that the recipient will not be able to answer you directly with their e-mail application, they must use this service following the same steps as you.
No personal information, email, etc. appears in this message: the only thing about you that appears is your Community Player's name.