Just go to coinbase.com and click on “Register” at the top right.

You will then arrive on this page (below) where you will have to enter your Name, First Name, E-mail and choose a password.
You must use your real personal information.
Make sure you choose a fairly complex password.
Confirm your e-mail address by clicking on the link that was sent to you on the address you indicated.

You must then indicate if you are an individual or a company.

To buy crypto-currencies with your euros freshly deposited via bank transfer, simply go to the “Buy & Sell” page.
Choose the currency you want to buy and enter the amount in euros or bitcoins and validate the transaction by pressing “Buy Bitcoin Immediately“.

To buy crypto-currencies with your credit card, you can also go to the “Buy & Sell” page.
Enter the details of your credit card, choose your cryptocurrency, enter the amount you want, then confirm the transaction by pressing “Buy Bitcoin Immediately“.
(There are limits of amounts with credit card purchases on Coinbase 100 euros / day at the beginning then 500 euros / day thereafter)