For example, the Romans spelled Claudius as Clavdivs. When was v replaced with u, and what symbol were the romans using for what we use "v" for today. Thank you for your time.
In actuality, we didn't really "replace" V with U. Instead, V was split into V and U, depending on where in the word it was used. This started sometime in the late middle ages, probably not earlier than AD 1300.
From Wikipedia's article V: During the Late Middle Ages, two forms of 'v' developed, which were both used for its ancestor /u/ and modern /v/. The pointed form 'v' was written at the beginning of a word, while a rounded form 'u' was used in the middle or end, regardless of sound. So whereas 'valor' and 'excuse' appeared as in modern printing, 'have' and 'upon' were printed as 'haue' and 'vpon'. The first distinction between the letters 'u' and 'v' is recorded in a Gothic script from 1386
[edit] To answer your question about what the Romans used for "V," they used "V". Someone with some more linguistics chops can probably provide more information on this, but the letter V was used for V, U, and W sounds, I believe, and so there was just no need to use "U" for anything.
Sorry for bumping up an old thread, but it seemed better than making a new one.
My question is how do we know what the original pronunciation of certain words were? For example, the Claudius from the OP. How do we know his name wasn't actually said as Clavdivs, or Clavdius?
Another example, "DIVI F AVGVSTVS", I would say it as Divi Augustus, but could it have been Divi Avgustus or something?