We're gonna start with the writings of the apostle Paul.
Romans 12:2-Do not be conformed to this world, but be transformed by the renewal of your mind that by testing you may discern what is the will of God, what is good and acceptable and perfect.
We've gotten the "can we conform with the world?" question out of the way. No, you can't be of the world and follow Christ. Luke 16:13 say you cannot serve two masters. John 15:19 says that if Christ chooses you, you are not of this world. You have to decide if the Bible is true or false. Strange as this may sound, if you get along with literally everyone, everywhere you go then you've probably conformed with the world in some way. Everywhere Jesus went people either flocked to him and idolized him or they wanted to stone him. There was no lukewarm good old buddy, "can't we just get along" going on.
Ads, media, music, politics, junk mail ads, your boss at work, your peers, friends and your spouse are things that satan uses to try to make us conform to this world. How many times a day do we have to tell ourselves that we are to be a choice race, a royal priesthood. How many times a day perhaps a billboard on the road will tell you how much fun you can have drinking alcohol or going to a riverboat casino? We hear radio commercials advertising the latest "R" rated movie and how it just can't be missed by one and all. Ads are everywhere telling us the latest birth control to get, to the latest and greatest beer. Fashion ads are telling us how to dress or be undressed so modesty is thrown to the wind. People just have a tendency to conform to these kinds of things if they think "everybody else" is doing them. Political ads and candidates want their opinions to be yours, and you're slow and unintelligent if you don't see it their way. Some music is promoting ideas that are completely contrary to the word of God. TV/Cable programs promote promiscuity, drinking, marital affairs, homosexuality, and the bad guy actually gets by without paying a price sometimes. God's people have to know when they are conforming to the world. They have to know when to say no to something.
We have to conduct our actions and language as if Christ himself were sitting right next to us. How many people would get in their skimpy bathing suit/bikini (male or female) and sit down next to the Lord? Most sane thinking people would say that's ridiculous, they would never do that, but they don't mind going to a public beach and doing the same thing. What about bringing that "R" rated movie home with the Lord there? Would you try to take Jesus to the casino with you? Would you try to convince Jesus that the political issues of the day have to be compromised on such as abortion and gay rights just so we can get something done? All of these are ridiculous questions. I could never name all examples of conforming, they're as vast as this world itself. Christians that spend time in the Word will recognize conforming when it rears its head. Christ himself said in Revelations chapters 2-3 when speaking to the seven churches, "I know thy works" and he knows ours.
If you allow all these things to subvert God and compromise to something between God and the prince of this world, Satan. Satan wins.
The flow of this world is with the grain.
As Christians we have to go against the grain.