Hi,
hard to tell what strategy you're attempting, as generating faith and conquering don't need to go hand in hand; I'll give a quick rundown on the methods to Culture Victory just to try to cover all the bases and answer your question:
1) The "Standard" Way
How to Generate Tourism: Build culture-producing buildings (amphitheater, opera house, museum etc.) and wonders (Parthenon, Sistine Chapel, etc.) and then fill them with Great Works you create with Great Artists, Writers, and Musicians, and also with artifacts you dig up with archaeologists. These Great Works generate your tourism. Later buildings like airports and hotels also significantly boost tourism.
Conquest?: Not necessary, and often detracts from your tourism creation; however, each AI civ you wipe out makes it easier to win by having one less civ to be influential over. Can't conquer them all though, as that is a domination victory
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2) Build Sacred Sites
How to Generate Tourism: Get a religion and choose the beliefs that let you build sacred buildings with faith (Mosques, Pagodas, and/or Monasteries). Then go down the Piety Social Policy Tree until you get Reformation. Choose the Sacred Sites reformation belief and you will generate 2 Tourism per faith building.
Conquest?: Same as above-- Not necessary, and often detracts from your Sacred Site creation; however, each AI civ you conquer, makes it easier to win.
3) Using Liberty and AI Liberation
(100% credit goes to Vadalaz for figuring out this possibility!)
How to Generate Tourism: You generate tourism generally in one way at one time-- Have a Great Musician do a Concert Tour in a civ that has less than 100 culture, when no other AI civs are remaining in the game.
Conquest?: Here is the process: Conquer an AI civ before it gets to 100 culture; Then wipe out all the other civs but one; Then gift the sub-100-culture capital to the last remaining Civ. Hopefully that civ will liberate the sub-100 culture AI civ and bring it back into the game. You then quickly destroy the liberator civ before the sub-100 culture civ gets over 100 culture. You have a Great Musician (obtained as reward for completing the Liberty SP tree) do a Concert Tour in the sub-100 culture civ. The tour creates a default value 100 Tourism Points even though you are generating no tourism. If that civ is still under 100 Culture and is the only AI civ left in the game, you win!
I usually call this the Greek Liberation strategy as Greece is one civ that will reliably liberate a capital gifted to it more often than not. Gifting other civs that sub-100 culture capital often will not get the city liberated and thus the strategy is moot.
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That's it, in a nutshell. Hope it answers your questions.