An excellent exposition of the three pronunciation types on youtube: link
And an online Classical grammar here: link
Three types of Latin pronunciation exist: Classical, Ecclesiastical and English
Most of the letters are the same throughout, except C, G, H and V.
In Classical latin:
C is always hard (as in "cat")
G is always hard (as in "gate")
V is pronounced like "w"
H also sometimes pronounced like "k", but that's not a letter that causes much aggravation to people
In Ecclesiastical Latin (the one in current usage and the Latin of Linnaeus, and as modern Italian)
C is soft before E, I, AE and Y (as in "cello")
G is soft before E, I, AE and Y (as in "gel")
V is V
In English Latin the same as Ecclesiastical except
Our soft C is lke an "S" - as in "cell", "ceiling", "circle"
So Cicero is pronounced:
Classical - kikero
Ecclesiastical - chichero
English - Sisero
This doesn't touch on transliteration of Greek letters, of course, which sadly make up maybe 90% of all Latin names so that, for instance, Greek kephalae* becomes confusingly cephalus - hard Greek C or soft Latin one? And it doesn't cover the fact that CH is always hard - whether it's Latin of any sort or a transliteration of the Greek letter Chi, which is pronounced like the"ch" in Scottish "loch" (Chapter 1, any Greek grammar). Examples are araCHnid, arCHaeology, psyCHology, sCHism, and so on (and for Italian CHianti and BrusCHetta - and yes it IS hard in Bruschetta!)
I'm sure none of this will help any of the differences of how people actually try to say Latin names. Most people understand most of the time, and particularly when it's written down!
* note that while "-ae" is a plural ending in Latin it's a feminine singular ending in Greek