Currently, you can't transfer a token directly on the Async site. However, you can easily do this using Opensea.
Go to Opensea and make sure you're logged in with the same ETH address that you use on Async.art. (if you use Email to log in on our site you won't be able to do this).
Go to "My Profile" which you'll find in the dropdown under your name in the upper-right:
Find the token you want to transfer in your collection and click it to see the main page for it. Once there you'll see this gift icon in the upper-right. Click this.
On the next page you can provide the address you want to transfer to. If you want to burn the piece you can send it to this address:
This address isn't owned by anyone, so no one can access any tokens sent here. That's why this is commonly used for burning tokens.