First open your ePoster (Click on the Preview in the Editor or click on its Title in the Showcase) . Then click on the More Menu (1) and choose Share (2).
You can now click on the Share on Twitter button (3) to share this ePoster/Stack to Twitter.
You will be asked to sign into Twitter (if you are not already signed in) and a draft tweet will be created containing the unique web link (4) for your ePoster/Stack. You can edit this tweet as you want before pressing Tweet to post it.
Please make sure that your ePoster has been published or you have made it public (by changing its access permissions) before you share it.