Prerequisite:
You know how to create a Plezi contact list, otherwise you are back to square one.
To export all your contacts, choose the condition "Contact property > Email > Is filled in".
Once your list is created, just click on the download icon at the bottom right of the app:
Then go to your e-mail box, an e-mail is waiting for you to download your export file (.csv) ;) (the more contacts you have in the list, the more you'll have to wait since the file will be more heavy :)
Tips and Tricks!
Is your export unreadable? Don't panic! The "csv" format may not be recognised by your computer. If so, you have plenty of articles in Google to help you with that, here's one that is very complete :)