I don't know all of the victory conditions by heart, but since no one else responded I'll see what I can do (and I have to work on memory since I don't have the game installed here). I hope this helps.
- Altar of Luonnatar (hope I spelled it right): Your Civ must be Neutral or Good. I don't know the necessary research you need for each stage so you'll have to look that up on the tech tree yourself. The altar has 7 stages. The first six are built instantly by using Great Prophets. The last part needs to be built like a wonder, depending on the production capability of the City this will usually take between about 25 to 80 turns. I'm not 100% certain but I think all parts need to be built in the same city.
Note that all remaining AI controlled evil Civs in the game will automatically declare war on you after you completed Stage V of the altar.
- Conquest: straight forward, completely destroy all other Civs in the game by taking all of their cities
- Cultural: Three of your cities need to reach Legendary Culture (50,000 culture points in each)
- Domination:you need to control 66% (I think) of the worlds population and 66% of the total land mass
- Gone to Hell: 90% (or maybe just 80% ?) of the world must change into hell terrain (this process starts after Infernal Pact calls the Hyborem into the game) and you must be the strongest (most total points) of the civs responsible for this process.
- Religious: Including your own Civ, 80% (I think) of the world's population needs to follow your state religion (I never tried a religious victory so I am not sure if you need to be in control of the holy city... hopefully someone else can clear up that point).
- Tower of Mastery: Anywhere in your Civ (these don't need to be in the same city) build the Towers of Magic (Tower of Alteration, Tower of Elements, Tower of Divination, Tower of Necromancy), you need access to all of the mana in each group to build the corresponding tower and you need access to the mana until the tower has been built (if you lose your only source of one of the necessary mana while the tower is still built your city will stop building it - after it has been built you don't need the mana any longer so you can dispel your nodes and build the nodes necessary for another tower).
After all of the above mentioned towers have been built (and provided you don't lose one of the cities that has one of the towers) you can at any time start building the Tower of Mastery in any of your cities. Like with the altar this usually takes between 25 to 80 turns.
Note that as soon as you start building the Tower of Mastery all remaining AI Civs (regardless of alignment) will declare war.
I'm not sure what the Quick versions of these Victory conditions are all about.