Couple of questions
In German - Guten Tag is a very common expression , and in english translates to good day. However, good day in english speaking countries is quite antiquated and is now rarely used anywhere. People generally would use good morning or good afternoon. Which brings me to another question - In German -good afternoon is Guten Nachmittag, which unfortunately is apparently antiquated in German. I have heard it, but apparently it is bad form to say Guten Nachmittag outside of a classroom setting. Any other comments on Guten Tag and Guten Nachmittag? Das ist alles!
"Guten Tag" - you could say all day long
"Guten Morgen" - you would say mostly before 11 a.m. or until lunchtime, but never after noon/lunch time (except you have forgotten the time and you don't realize that it's already that late).
"Guten Abend" - you would usually not say before 5 p.m., maybe also starting to use it a bit earlier if your workday is already over
"Gute Nacht" - you would only say when the day is over, never as a "hello", it is only used as a "farewell" (when you or the other people are supposed to go to bed after you leave each other). If it's already night time and you want to say "hello" you should use "Guten Abend" instead.
"Guten Vormittag" / "Guten Nachmittag" - is not uses as a "hello" but as a "farewell" it might be used in a sentence like:
"Ich wünsche dir (noch) einen guten Vormittag/Nachmittag."
Short (do not use in written language): "Guten Vormittag/Nachmittag noch".
However, it's more common to use "schönen" instead of "guten" here.
And, you would only use this phrase at the begin of the morning, e.g up to 10 a.m. Later it would rather be "Schönen Tag noch" / "Einen schönen Tag noch".
"Guten Nachmittag noch" you would only use as long as "Abend" does not approach, yet, e.g. until 16 p.m. Later it would be "Schönen Abend noch"
Until lunch time: "Guten Morgen" / "Guten Tag"
During lunch time (at least in some areas of Germany) you could also here "Mahlzeit!" (which literally means "have a nice meal")
After lunch time until about after tea time: "Guten Tag"
After work and during the night: "Guten Abend" / "Guten Tag"
- When you're about to leave for going to bed: "Gute Nacht"
I'm a native German speaker and I've never heard someone saying 'Guten Nachmittag' in a serious way (but maybe joking).
You can also say 'Guten Tag' when it's morning or evening, e.g. when you greet someone you're passing by. I feel like 'Guten Morgen' or 'Guten Abend' can sound somewhat too personal when used in a very formal setting.
What is indeed a bit antiquated is saying 'Guten Tag' when leaving. I heard it in old movies and was confused. ;) I think you could still hear it in formal settings.
Mia797420 explained really good what we use in German. The "Nachmittag" as a time is not really so important anymore in our daily life here I think. A lot of people live their daily working during the day and stop in the Afternoon or evening and they mostly ask more what someone is doing in the evening or after work/ school... than what he or she is doing in the afternoon.
The "Nachmittag" is often seen as a time like a bridge between the middle of the day and the evening where old people eat cakes and coffee or children have a short time together till they have to be at home and things like that.
Nachmittag can still be quite useful to state a time span like "Ich saß den ganzen Nachmittag in Meetings" or "Was machst Du am Samstag Nachmittag, wollen wir Radfahren gehen/ein Fußballspiel anschauen?". Those are totally common phrases for me...
I can't remember that I've ever heard it in a greeting like "Guten Nachmittag", though.