Do Germans say "Guten Tag"?

Yes, Germans do say "Guten Tag" and it is a very standard, polite greeting meaning "Good day." It is pronounced "goo-ten tahk" and is used throughout the day from late morning until evening, roughly from 10 am until 6 pm. It is more formal than "Hallo" which is like hi. You will hear "Guten Tag" constantly in professional settings, in shops when entering, at the doctor's office, in emails as an opening, and when speaking to strangers or older people. In northern Germany people often shorten it to just "Tag" pronounced "tahk" which is a casual version. In southern Germany, Austria, and Bavaria, people are more likely to say "Grüß Gott" or "Servus" instead of "Guten Tag." While "Guten Tag" is correct everywhere, young people among friends will almost always say "Hallo," "Hi," or "Na?" instead. So if you want to sound polite and respectful, especially to someone you don't know or in a customer service context, "Guten Tag" is perfect and very natural. It is often followed by "Wie kann ich Ihnen helfen?" meaning "How can I help you?"