"Following Christ" means that you try to live your life according to his teachings and the Bible, and you develop a relationship with him and live by the Holy Spirit. It's about "dying to self" and allowing Christ to take over your life. "I must decrease so he can increase" is the saying.
We can have a relationship with him after we admit we're flawed and he's not, and that he died in our place so we wouldn't have to pay the penalty for our screw-ups. We all screw up -- I tend to jack things up on a regular basis. The cool thing is because I've accepted Christ as my Lord, when I stand before God the Father and I'm held accountable for my crap, he'll see Christ and his perfect life instead. That's because of the work of the cross, which is beautifully explained in "The Lion, The Witch and the Wardrobe."
Although you're set aside, or "saved" from your sins as they say, once you accept Christ, you're on your way to heaven. (i.e. the criminal who was crucified with Christ that we hear about in the Gospels.)
However, eternity is now.
A relationship is what God wants with us. I myself strive (and too often fail) to do my part in the relationship (God, being God, always does his part.) I try to begin my days with prayer (both talking to and listening) and with some Scripture reading and meditation. I try to live my days in love, because God is love and to love another is to see the face of God.
It's funny that a relationship with God is easier than most relationships with humans on one hand, but more difficult in other aspects. It's worth it though. When I'm focused on him and I'm seeking to live out his will for my life, my life is lived to another degree. But it's because of him living in me, not anything I'm doing.
As far as Mormons go, they're NOT Christian. They claim to be, but they're VERY different. Their interpretation of the Bible is VERY different from Christianity. They don't believe in the Trinity -- that there is one God in three persons (Father, Son and Holy Spirit), and this is essential Christian doctrine. They, in fact, believe that we can achieve God-hood. With all due respect, this is absurd.
They also believe you get to heaven through Grace and works, meaning through Christ's death AND through your own efforts. These two elements contradict each other though! Christ died on the cross because God knew we can't do anything to become righteous. We can't pay the penalty of death for our sins, but God can, and did, through the death AND resurrection of Christ (who was fully God and fully man). "We all fall short of the glory of God," says the Bible.
Mormons also believe in baptizing the dead, which is another gross misinterpretation of the Bible, and a number of other odd things. There's also never been any geological find to support the Book of Mormon, but there's been countless and continual finds supporting the Bible.
The Bible also warns against those who preach a different Gospel, which is unfortnuately what they do. They have a hard time responding to this verse.
However, I must say, many of them ARE nice people and they mean well. Their missionary work (i.e. going door to door on bikes spreading their stuff) is commendable. What they're spreading is questionable though.
I’m sorry this is so long and winded, but I hope it helps. To the Mormons in the house, I speak in love.