In this high level overview, the Etherboost team which is behind EtherDelta wrote:
The EtherDelta smart contract allows you to deposit or withdraw Ether or any ERC-20 Ethereum token.
If you go to the EtherDelta page, you can click on Tokens (in the top navigation bar) and see the list of all the tokens that are currently traded.
As to the process by which a new token gets listed on EtherDelta, I could not find any published information about what the steps are, so I would recommend getting in touch with them directly to ask. This really informative Stemmit article here about how to use EtherDelta lists several places you could ask that question:
...if you have any questions you can get in touch with them:
I emailed Etherboost to ask for clarification about how an ERC20 token gets listed on EtherDelta, and here is the answer I received:
On Jul 19, 2017, at 4:01 PM, Zack Coburn wrote:
Any Ethereum-based token can be imported as a custom token and start trading on EtherDelta, without permission.
To appear on the list of official tokens, the token owner/creator should email email@example.com with the following information:
a. Token address (code should be verified on Etherscan) b. Official
Web site (the token address should appear on the official Web site for
verification) c. Paragraph description of the token.