Historically, there were two different pronunciations of Latin, classical (said to be the way the original Romans pronouced it) and traditional (or mediaeval) Latin. It appears that today we have the third way, the "ecclesiatic" Latin heavily influenced by the Italian pronunciation.
The diferences between the former two are relatively small, and effectively make the classical Latin sound more like anceint Greek.
For example, in classical Latin:
- c is always pronounced K;
- diphthongs ae and oe are pronounced "ai" and "oi" (or "ah-ee" and "oh-ee", only the composite sounds are short);
- "ti" is always pronounced at "ti" (tee);
But in traditional Latin:
- c is is prnonouced as K, except when it precedes vowels e, i, y, or diphthongs ae or oe in a word, when it's pronounced like a "ts" sound (like the german "z" in Zeit, for example, english doesn't have this sound);
- diphthongs ae and oe are always pronounced as a long "eh" sound;
- "ti" is pronounced as "ti", except when it precedes vowels, but is not following s or x, when it's pronounced "tsee"
Common to both pronunciations:
- i is pronounced as a consonant y at the beginning of a word (but in traditional Latin, diphthongs ae and oe can be pronounced as ay or oy as well);
- q is always followed by u, and is pronounced as "kv" (don't know how to describe this, I can't think of an equivalent in any language except Croatian, and I just wrtoe that)
- ph is f
- ch is h (a bit softer than that in Loch or german Ich)
- rh is just r (but not the english r)
- th in words of Greek origin is th, pronbounced so that both t and h sunds are heard
- ngu is pronounced ngv when preceding a vowel
What fusangite describes is the ecclesiatic pronunciation, except that I've never heard of the "w" sound used in Latin. The "c being english ch if followed by an e or i" is obviously heavily influenced by the pronunciation in Italian, since it's taken pretty much directly from that language.
Take for example the word "medicina" (strangely enough, it means medicine

). In classical Latin it's pronounced [me-dee-KEE-na], in traditional "medicina" [me-dee-TSEE-na], and in "ecclesiastic" [me-dee-CHEE-na]. It's really easy to see from which pronunciation the modern word "medicine" came.
As for the accuracy of pronunciation... well, we can't be a 100% certain for classical pronunciation, but it's very close to that. There's really no doubt regarding traditional pronunciation, really, as it has been actively used till very recently (as an interestng fact, Latin has been the official language in most of Croatia for a very long time, and in fact, the first speech in Croatian held in croatian parliament didn't happen till 1848, IIRC; also Latin has been the language of nobility in the Lands of the Crown of St. Stephen, or the Hungarian half of the Habsburg Monarchy).
As an additional point of interest, in Croatia, coastal areas primarily use traditional pronunciation, whereas inland areas use classical (at least it was so during my high school days).
And, finally, to concur with the answers given to the original poster, dius is indeed pronounced "DEE-oos".