I believe EtherDelta is one of the very early working decentralized/distributed exchanges (based on ETH). As a result there are some difference compared to centralized exchanges such as Bittrex that causes some confusions for first users.
Below you can find a step-by-step instruction on how to use EtherDelta:
In the main page (https://etherdelta.github.io) click the drop-down EtherDelta (Private Key) on the upper right corner and click on "New Account":
This will pop up a window similar to the one below. Before click "OK" make sure you save your private key in a secure way in case of losing access to EtherDelta:
NOTE: I would copy/paste both public & private key from this window and save in a spreadsheet, since in EtherDelta you will not be able to easily highlight the public key later on to deposit Ether).
Use your EtherDelta Pub. Key (Ethereum account above) to transfer your ETH from external wallet into your EtherDelta wallet.
Select the appropriate crypto from the drop-down menu shown below (the crypto that you want to trade):
In EtherDelta there are 2 types of wallet. One is your personal wallet and the other is EtherDelta Wallet or Smart Contract, as shown below as Wallet & EtherDelta respectively:
You need to deposit your Ethereum from Personal Wallet to the EtherDelta wallet using the Deposit button:
If you also can't see the "BUY" or "SELL" button at the bottom of the screen you can simply click on the red orders in the ORDER BOOK to Buy or green orders to Sell (depending on ETH|Crypto exchange rate you want to trade in) or click on PPT field and tab it down to the "Buy" button at the bottomw:
If you selected a correct amount that also covers the exchange fee you should see the following message and the "Pending" order in "My Transaction" window:
After you place an order you should be able to see your order in the "Order" tab in the "My Transactions" section:
To move your "new bought" crypto to your "Wallet" in EtherDelta use the "Withdraw" button and specify the amount you want to transfer.
Finally to move out your funds to an external wallet you need to first withdraw your funds to your wallet first (as described in step 6) and then use Transfer tab to transfer your funds to another wallet: