One of my favorite quotes is "Your greatest weapon is in your enemies mind." I think its a Buddha quote, I may be wrong. But my point is, to completly obliterate your oponents debate, you must first know thier material. The better you know your oponent, the better you will know how to counter them. What I get from your post, you are debating against the Mormon religion. First, know the Bible, and also the Book of Mormon. Come up with questions that are difficult to answer. Also, know any contradictions, because one of the best things to do to win a debate is to destroy your oponents credibility on the issue. If you can stump your oponent, you are on the road to victory. But be prepaired with possible counters, because if your hurt oponent hurts you, your the one with lower credibility. Sharpen your wits to a fine point to avoid this. After you have completly destroyed all credibility on the issue, or have come to a level you deem satisfiable, launch your own assault. From your perspective, hammer away at what they tried to argue. Counter thier counters, and leave it at that.
On the verbal issue of debating, you have to be a good and strong speaker of quick and sharp wit. The quicker you can come up with answers and questions, the better. Also, AT ALL COST, AVOID using words and phrases such as; "I think" Umm, uhhhh, etc.," and any other words and phrases that can level the debate, such as "what if your wrong" you say that, you admit there is a possibility your oponent is right. You don't want that. And as Prima said, a strong weapon for debating is citing highly credible rescources. Also, admiting something is your opinion kills your debate.
You must also be a great listener to debate. Listen to everything your oponent says, pick apart, disect it, look it over, then mentally find all flaws. If your oponent is right about something, admit it, then destroy it. An example is when I debated on physical discipline for children, my oponent said that pain is experienced, and it can often scare the child, which is not healthy. I replied, "Yes, a level of pain is experienced when the child is hit, but a child will experience pain from every day life. A child skateboards, falls, and skins the knees. A child climbs a fence and falls. Children get hit with balls, stung and bit by insects, shocked, and burnt. These do not teach the child fear, they teach the child boundries and care. A child who falls of a skateboard will learn get up, and try a different approack. One who falls of a fence will try different foot positions. A child will also learn to not mess around with bees that sting, the stay out of electrical outlets, and the value of wearing sun screen lotion." I killed the issue of pain being experienced. My oponent then said, "But then a child will learn a way to not get caught doing things that are wrong." To which I quickly responded, "Not if the parent or babysiter is properly supervising the child." My oponent couldn't counter that, and moved on to another point.
I can say the best way to prepair is prepair your main points, then several side points and key words, then think of as many as possible counter points and questions your oponent will bring up. Practice, even you end up debating against your self. And go in with confidence, know your right and thier wrong. If a foundation has a crack, it will crumble quicker than the foundation without a crack.