First a little refresher on ethereum :

private key : you wallet, never share it, keep it safe
public key : what you use to receive money, computed from your private key
smart contract : application that is coded and run in the ethereum blockchain
gas : use to pay for transaction fee, you often see "gas limit", because you cannot know in advance how much gas a transaction will consume, so you put a limit
GWEI : the price per unit of gas, 1 ether = 1 billion GWEI
transaction pending : when you emmit a transaction it goes into a waiting list, the mempool, while in the mempool the transaction is marked as 'pending'. Miners come and take some of them to put in their block, they take the transactions with the higher GWEI because they will earn more money this way, that is why using a higher GWEI value makes your transactions go faster.
etherdelta wallet : this is where you deposit/writhdraw money
smart contract wallet : this is where you need to put money to trade

Some info on etherdelta :

What is etherdelta? it's a smartcontract, noone can stop it, no one can alter it :o

Why is it nice? it allow you to trade any existing token of the ethereum blockchain, without any authority having to add it to the market, whithout any authority being able to stop you
So why can't I find some tokens? because etherdelta.com is a website that allow you to interact with the smartcontract, this website is centralized and people need to modify it to add new coins.
But you can trade a coin that has not been added to the website if you know the smart contract adress of the token.

Can I be hacked? not really, but you can input your private key on a false website, get it stolen if you send it by mail or stored it in a text file on your desktop.

How can I easily find tokens on etherdelta? go to coinmarketcap, look at bitdegree for example : https://coinmarketcap.com/currencies/bitdegree/

clic on the market tab, and then clic on the link to etherdelta :

How to use ETHERDELTA :

you do not register to etherdelta, you add a private key = an ethereum wallet.
DO NOT ADD AN EXISTING WALLET, create a new one, like this if you mess up (connect to a phishing website, have your key stolen from your computer) the thief won't be able to steal all your money, just what was on your etherdelta dedicated ethereum wallet.
this is how I do it : deposit eth on etherdelta wallet / transfert eth to smart contract / trade / transfert back traded token from smart contract to my etherdelta wallet / send tokens to my safe ethereum wallet
keep reading and it will make sense

1/ Creating a new private key for etherdelta

go to : https://etherdelta.com

clic on the upper left corner "select account" then select "new account"

Then this windows pops up :

the blue rectangle contains your public address, you'll use that to deposit money.
the red square contain your private key, do not loose this, do not email it, store it somewhere safe, this is the private key, your wallet, with this key anybody can connect to your wallet and steal your money.

if you somehow closed the popup you can display it back like that :

2/ increase the default gas price

Now before doing anything we need to do something else, remember etherdelta is just a smartcontract, meaning that to interact with it you need to make transaction.
The transaction will be faster if you pay more fee, to do that you need to increase the default GWEI to 50 (GWEI is the price of gas, gas is what is used to pay for tx fee, a tx with a 50GWEI usualy cost me 1.7$, yup, 1.7$ per action on etherdelta)

To increase GWEI go to the right corner

this then pops up

Change it to 50, with a value of 4 your transaction will takes hours before being mined by the ethereum network :o

3/ deposit money on your etherdelta wallet

it can be ethereum or directly a token (ethos, bitdegree, etc), ok so use your favorite wallet, for example my etherwallet
did you know that you can download myetherwallet and run it on your computer? like this you are always safe, just download the zip file, unzip and clic index.html
https://myetherwallet.github.io/knowledge-base/offline/running-myetherwallet-locally.html
Anyway, I just sent 0.07 ETH to my etherdelta wallet, the left upper corner now look like this :

So now we need to deposit this money into the etherdelta smartcontract in order to be able to use it.

But you CANNOT deposit the whole 0.07ETH, remember that each operation is a transaction? transaction cost gas and thus cost ethereum, those cost will be taken in the red rectangle, so you always need to keep some ethereum into it.

I now deposit 0.05 eth in the smart contract by typing 0.05 then cliquing the deposit button :

this pops up :

clic on the text in the red square in order to check it out in etherscan, once you transaction gets out of the mempool it will start having confirmation and then it will show in etherdelta
once it show you'll end up this this :

as you can see the 0.05 eth were deposited in the smart contract, and I'm missing 0.002 ETH from my wallet :o which is normal, it is what the transaction costed me.

Congratulation, you can now start trading.

4/ buy something

ok let's buy some tokens, this is the order book :

in red it's the people selling, in green the people buying.
BEWARE, there is no protection like on classical exchanges, on a regular exchange if I say "I want to buy takenA at 1$" and someone is selling some tokenA a 0.4$ a piece the the exchange will buy them a 0.4$ and not 1$ like I asked.

On etherdelta it buys/sell at whatever price you input, if you miss a zero you could loose a lot of money.
Back to buying, clic on the first red line, this pops up :

input the number of token you want to buy and clic buy. then you get an other popup

as usual it makes a transaction to process your operation (buying token) this will need as before to get some confirmation and it will eat some eth of your wallet
then :

So now you transaction is confirmed and you just bought tokens, you then have to get them out of the smart contract and then back to your main wallet

5/ getting the token out of the smart contract

clic on the withdraw tab

iinput the amount you want to get out and clic withdraw

Once again a transaction is created, wait for confirmation, it will eat some of your eth

Ok so now the tokens are out of the smart contract and in your etherdelta wallet :

6/ transfert those tokens back into your ethereum main account

clic the transfert tab

Input the amount of token you want to withdraw, input your main ethereum wallet address, clic withdraw

Once again a transaction will be created, yadi, yada...
And voila, you just bought tokens on etherdelta :)
Something wasn't clear? want me to explain something else about the technical side of cryptos? ask in the comments!