For travellers who want to enjoy more of Europe - particularly of the countries within the Schengen area -, and less of the crossing points, getting the visa(s) and paperwork right is a must.
If you are traveling from Asia, Africa, South America, or Oceania to any of the Schengen territories for 1 to 90 days, you'll probably need a Schengen visa. This visa will allow you to enter the country you are traveling to and for little to no difficulty when crossing over into other countries within the Schengen area.
The first thing to do when traveling to one or several of the Schengen territories, is to go to the embassy or consulate of the country in which you will be entering the Schengen area to check if you actually need a visa. If so, you'll need to apply for a Schengen visa. For this, you'll have to fill out some paperwork and notify them of your main destination and trip plans. It is the embassy or consulate from the country where you will be first entering the Schengen area that will be responsible for granting your visa, and for allowing you to pass through the different territories.
Have in mind that getting a Schengen visa can take up to several months. So, plan your trip and apply for your visa ahead of time to avoid any bad surprises.
Most of the Schengen visa requirements not only call for the permission from the country(ies) you are visiting, but also specify that responsibilities for you traveling in their territory(ies) are taken care of. The later is mainly linked to the need of having a Schengen visa insurance that will provide you with travel and health coverage in the event that something unfortunate takes place during your trip.
The Schengen insurance should cover both travel and health expenses while you are moving through Europe. This requirement is mandatory to apply for a Schengen visa and can also be checked at the main Schengen border points.
The Schengen visa requires a minimum health coverage of 30,000 Euros (around $45,000 USD) in the case of an injury, accident or illness. If needed, when traveling through the Schengen territories, this amount should allow you to get proper medical assistance.
Regarding travel coverage, it is requested that the insurance covers any unlucky situation that may arise like the need of medical repatriation, rescue expenses, or bodily and/or material damage caused to others by yourself (civil liability).
It's important to note that the Schengen insurance can not expire while you are traveling through any of the Schengen territories.
Finally, another factor to look into is that the insurance company you buy the Schengen visa insurance from is represented by an office within the European Union. This will make a lot easier to get proper service in case of an emergency.
Have a nice and safe trip!