During a national strike, all transportation may be stopped or experience a slow down and sometimes museums may be closed as well. National strikes are fairly rare. Strikes may even occur in sympathy with strikers from other countries.
How can you find out about an upcoming sciopero? Strikes are planned and announced in advance. For example, if there is going to be a train strike, the date and time is usually posted at the station several days ahead. Look for the word sciopero on a sign at train stations, metro stations, and bus stops. It probably won't be in English but you should be able to read the date and times.
You can ask the local tourist office or your hotel (they probably won't volunteer the information unless you ask) for information about strikes if you're planning to travel.
Here's a site that has a calendar of Scioperi. Although it's in Italian it is pretty easy to understand.
Nancy, about.com's guide to Senior Travel, says, "Summer travelers to Italy should beware of strikes around August 15, the date the entire country goes on summer vacation. That’s a classic time for labor unions to declare strikes."