Settling down in Spain should be easy for EU members but you'd be surprised at how complicated it can get!
The first and most important task is to get your NIE number. that will get you started in the system. When you fill in forms online or offline, it can be compared to the DNI or Residency ID. There is a certificate which comes with the NIE which gets sent to your home address or to the police station where you requested it.
If you want to start working the NIE often is sufficient, but you'll also be asked to register with the Town hall. This process is called the padronamiento. This will get your name on the resident list, and they should send you documentation with where your nearest public doctor is and finally you should get your social security card which you'll need for work purposes.
With the NIE and the empadronamiento you're set to live and work in Spain. In theory that is! In reality you'll find loads of obstacles if you don't have the residency card. Some banks will refuse to give you a checking account without a residency card. Only a "non-resident" savings account will be granted. Some driving schools won't allow you to take the practical exam and many times when you are asked for your DNI they just don't get it, that the NIE is suficient.