The only thing really needed to travel within the law in a foreign country are the documents. They vary depending on the country where we're going to spend our holidays or to make our trip. The birth of a United Europe a few years ago made it possible to simplify transfers within the continent but if we decide to visit a country out of this we will inform us in advance all the necessary documents.
If you travel within the countries of the European Union, thanks to the Schengen Agreement, it is enough to have an identity card. Currently, the countries in which you may travel with the only ID are: Austria, Belgium, Denmark, Estonia, Finland, France, Germany, Greece, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Poland, Portugal, Czech Republic, Slovakia, Slovenia, Spain and Sweden, plus Iceland and Norway (non EU). Ireland and the UK have not signed the agreement.
Cyprus, which joined the EU in 2004, and Bulgaria and Romania, which joined in 2007, not yet fully participate in Schengen. You will therefore need a passport or identity card valid for travel to these countries, as well as in Ireland and the UK.
If you rather travel to countries outside the EU must be equipped with passport (need at least 15 days, often more, to get at police responsibility). Always check in advance whether they need any special visas and vaccinations (the more "traditional" Yellow Fever, Hepatitis A, Hepatitis B, Typhoid, Tetanus, prophylaxis ... however it is always good to consult your doctor before starting and learn the Department of Medicine
The international driving license is available from the Motorization in about a week.Regarding health insurance, there are several states with which a convention is taking place and where you can get coverage through their mutual association. More information is available from the offices of the ASL premises.