Much of what I will be telling you I got from L'évolution grammaticale à travers les langues romanes by Sophie Prévost.

Basically, first you have to understand the basic concept of the evolution of language. Languages never really stay in the formalized literary form for long. Dialects and differentiation are characteristic of languages. An example that's well studied and that I have personal experience of is Pennsylvania's 5 dialects. Though it's all still english, there is specialized vocabulary and pronunciation in each of these dialects. The theory goes that, over time, these dialects become more distinct -- certain grammatical features develop, certain grammatical features fall into disuse based on how people use the language and need to express with it. Another factor that motivates language change is contact with another language, whether that be through contact by trade or being taken over. For example, the French language was deeply influenced by the flooding in of Roman and Germanic influence, brought in by conquerors, upon the original celtic languages that existed there. Languages like Spanish are deeply influence by vocabulary gained from several centuries under Arab Muslim rule. And nearly every language out there today is deeply affected by the pervasiveness of American english through media and business.

Latin is a language with a noun declension system. This means that the ending of nouns would be changed to convey its function in a sentence. Here are the declensions for the word cīvis (meaning citizen) in the singular:

Singular:

Cīvis - Subject of a Sentence

Cīvis - As a possessive (i.e. of the Citizen)

Cīvī - As an indirect object

Cīvem - As a direct object

Cīvē / Cīvī - as the Object of certain prepositions (A, Cum, Coram, De, Pro, Prae, Sine, e(x), and sometimes In, Sub, and Super)

There are more if the word is plural. This system allows you to, theoretically, not really worry about word order. However, over time, word order became more formalized and nouns had a much more states form, only changing between singular and plural (in modern French, for example, Citoyen is Citoyens in the plural). These new static forms were often the corrupted form of the dative/objective declensions (i.e., the direct object and indirect object). An example is the italian word from love:

The Latin word for love is amor. In the form of a direct object it is amorem. Modern Italian has kicked out the 'm' and turned it into amore. So the progression is:

amor ---> amorem ---> amore

Other words change just because of the pronunciation, after all, writing usually tries to approximate pronunciation (that's how we often figure out how words sound in Latin, by the way, the way it's spelled in older texts). Words like "Tiber River" were "Tiberis" in Latin, and over time the pronunciation for Tiberis became Tevere.

It's also important to remember that all of the Latin spoken in Rome did not become modern Italian. It first actually split into different dialects by region until you had separate languages -- Neapolitan, venetian, Sardinian, and Corsican are a few notables. The modern Italian language traces its roots to the Tuscan dialect of Florence, popularized by Dante Alighieri of Florence in his Divine Comedy. Dante's language because the language of the upper class in the Peninsula, and it only became a widely spoken language post reunification of the Italian peninsula from several kingdoms to one (though arguably, the seeds of this reunification, and the idea of having Italian as the language of the Italian peninsula was pushed by Napoleon Bonaparte, who was a strong supporter of the unified Italy. When he conquered it, he tried to push Italian as a common language.)

Hope this cleared some stuff up. Tell me if you'd like me to clear anything up!

I would recommend that you repost to lingustics reddits.