UPDATE: There have now been two episodes, the 50th anniversary special The Day of The Doctor, and the mini-episode "The Night of The Doctor", which deal with the events of the Time War. Both were released after this answer was written.
tl;dr: There are no television episodes that deal with the actual events of the Time War; The Last Great Time War as a concept was constructed for the modern series, and it occurred entirely off-screen in between the movie and the episode "Rose".
We do have some independent confirmation of many of the events that Nine and Ten have talked about (including from Davros, The Master, and Rassilon) and all evidence strongly indicates that the events were every bit as horrible as The Doctor claimed.
A number of classic episodes have subsequently been cited as related to the Time War in order to tie the classic and new series together, but those episodes do not contain any direct references to the Time War itself.
Although the seeds of the Time War apparently stretch back as early as the Fourth Doctor, as far as the events of the actual war, they took place entirely during his Eighth and Ninth incarnations. The Eight Doctor never appeared in a television episode, but even if you include the movie, the last he appeared "on screen" Gallifrey was alive and well and the Time War had not yet happened. The next time we see The Doctor on-screen, the Time War is over and he has regenerated (possibly very recently, as in "Rose" he is still seen observing his own appearance in a mirror.)
Most of the concrete information we have about the events of the Time War come from the Tenth Doctor, as he deals with other survivors of the war. He describes certain events that have already happened, but we do not see any of them. The closest we come to seeing the actual Time War is the Tenth Doctor's final episode, "The End of Time", where we are privvy to a war council including Rassilon and the other members of the High Council, just before The Doctor destroys them with The Moment. When the Time Lords attempt to escape the time lock, they bring many of the horrible things from the Time War with them, and there's pretty solid evidence that The Doctor was absolutely not exaggerating how dangerous those things were and why they had to be locked away.
However, while we never get to see the war itself, Russell T Davies has made an attempt to tie classic Who stories into the War. In particular, "Genesis of the Daleks" has been cited as the "opening salvo" of the war. In that episode, the Time Lords send the Fourth Doctor (and Sarah Jane) to Skaro to try to prevent Davros from actually creating the Daleks. This is the closest classic Who ever comes to anything like the Time War -- the reason the Time Lords send The Doctor to Skaro is because they have seen a future where The Daleks destroy Gallifrey. (There's a nod to this episode in the Tenth Doctor episode "Stolen Earth" when Davros recognizes Sarah Jane.)
The BBC has put together an audio documentary, The Dalek Conquest, that attempts to tie that episode and many other classic Doctor Who Dalek-based episodes into a coherent storyline that leads up to the Time War. It includes references to episodes dating back to Series 2, with the Daleks trying to kill the First Doctor, with the implication that the Dalek's have been planning this war since the beginning. Again, none of those episodes actually contain references to or depictions of the Time War, but they do represent some attempt by the BBC to tie old and new canon together (as much as you can with Doctor Who.)
There are also some other audio stories, graphic novels, and almost certainly some regular novels dealing with these events, but I haven't dealt with those much personally so I don't know exactly.
On a side note, there is a series of books dealing with the Eight Doctor's adventures that includes an epic conflict that is referred to as a Time War. According to Word of God, this is a Time War, but is not The Last Great Time War - it is more properly called the "Second War in Heaven" and is not the conflict that results in the destruction of Gallifrey.