In BSG when do we learn the assigned Cylon numbers for the models? As a latecomer to the series, I hear people refer to cylon model numbers, but I am curious what episode those designations (e.g. Sharon = #8) started appearing.
The first time a model is indicated by number is during the mini series that kicked off the show. Caprica six explains to Baltar that there are 12 Cylon models, and that she is "6".
Throughout the series, the models refer to each other by model numbers (in particular the 1's who seems to like the non-human designation). For example when debating the votes they said that the Number Ones, Fours and Fives voted as a block.
Most Cylon number designations are reveled within a episode of their true nature being shown.
The only exception of course is the Final Five, who have no set designation (they do not know what order they were produced in).
PS: It seems to be that the number is corresponding to the order of creation. We know the 1's were first for sure.
In the TV series the human-form Cylon models are revealed slowly (both their appearance and their model number), this was done deliberately to preserve the mystery/tension and give the viewer a Colonial-viewpoint (they don't know who the humanoid Cylons are).
As to which episodes the model number were first used, assuming an un-ambiguous setting and an actual number used rather a name or the Colonials realising the person was a Cylon (seeing a duplicate), this answer could vary greatly and I suspect could only be done by watching the episode in turn until all 12 are account for.
This Wiki page (contains spoilers) has a great deal of info (including pictures) on each model.
They do this to lead up to the Final Five, which is a big deal later in the series. We know that their are 12 models, so to bring up the topic of The Final Five, the series identifies the other 7. If you haven't watched too far, don't go too far into searching for the Final Five as it might ruin some shows for you.
It is here and there and hinted about. Not sure how much you want to learn before you watch but the numbers and models are out there and can be found on the BattleStar Wiki http://en.battlestarwiki.org/wiki/Main_Page
I am not sure where you are but later you will hear the numbers more and more. You might ask why if only 7, is there mention of #8? I believe that is mentioned a bit here and there but cleared up after the last of the final five is shown. The #7 line was destroyed by #1.