Hello Pat,
Many sunspots, especially the bigger ones, can be seen by the naked eye, if one is foolish enough to look without some kind of protection. It is indeed true that there are records from CHinese astronomers discussing dark spots on the Sun, dating back to 28 BC and perhaps further. It is not true that Galileo discovered sunspots however. Thomas Harriot and Fabricius had published results recording sunspots in 1609-1610 a year or so before Galileo's recorded observations. Christoph Scheiner was also observing sunspots around 1611. Galileo did claim to have discovered them but the hostorical records prove otherwise. Galileo was the first, I believe, to point out that sunspots were in fact on the Sun rather than a phenomenon of Earth's atmosphere or the passage of Mercury in front of the Sun.
David