These are the arguments for the existence of God I find most compelling. There are others. Use what appeals to you, the ones you find compelling.
(Bold is for subject headings. Normal text gives the thumbnail of the argument. Italics gives explanatory comments that you can go into if time allows and if necessary.)
1. The Cosmological Argument
A. Whatever began to exist has a cause. The universe began. Therefore the universe must have a cause.
Something cannot come from nothing. Even subatomic particles that arise from vacuum fluctuations aren't coming from "nothing" but from an energy-rich quantum field. If anything has ever come from nothing, anything can come from nothing.
However, God doesn't need a cause because God did not begin. There cannot be a continual, infinite progression of causes. It must stop somewhere. True infinities do not exist. There must be a first cause, and that is God (see B).
But the universe did begin. That the universe began to exist is a necessary result of the Second Law of Thermodynamics and General Relativity (among other physical observations). It is simply not possible that the universe has always existed.
If the universe didn't always exist, and if something can't come from nothing, something created the universe.
B. If the conditions for the creation of the universe were always met, the universe would have always existed. The universe has not always existed. Therefore some condition had to change. The physical conditions could not change, so it had to be a decision on the part of the creator — thus the creator has to be personal, not simply some force.
2. The Design Argument
The fine-tuning of the universe is due to either physical necessity, chance, or design. It is not due to physical necessity or chance. Therefore, it is due to design.
The design in the universe is unmistakable. There are dozens of physical parameters in the universe that have to be just so before life — any life, not just human — is even conceivable. One example is the cosmological constant which drives the expansion of the universe. If it were different by one part in 10 to the power of 120 (or 10^120; 10^9 is a billion) life couldn't exist.
These numbers don't have to be anything like they are, but if they weren't what they are, no one would be here. The odds of all of them being what they are simply by chance are beyond ridiculous — it would be like one person winning the lottery millions of times.
Therefore the features of the universe that make life possible must have been designed by an intelligent, personal designer.
3. The Moral Argument
If God does not exist, objective moral values and duties do not exist. Objective moral values and duties do exist. Therefore, God exists.
Notice that this is NOT arguing that atheists cannot be good. It's arguing that if God doesn't exist, there is no such thing as objective "good." If humans are just unusually advanced animals, murder is not wrong. One man killing another is no more wrong than a lion killing a gazelle. There is no moral obligation to help each other. Selfishness is nothing worse than the lion failing to share with the hyena.
But we all know instinctively that murder is wrong. Rape is wrong. Stealing is wrong. It is good to help people who are in need. We feel bad when we do wrong and when we fail to do right because this morality is ingrained in us. When someone does evil we do not respond as if the rules for a well-functioning society have been violated. We respond as if something evil has been committed. Those few who seem not to recognize morality do not disprove morality any more than the colorblind disprove the existence of color.
This inborn, universal knowledge of objective moral values and duties shows that God must exist.
The above only proves that a god exists. It takes more to prove the existence of the Christian God. For that you have to move from here to the case for believing the Bible and for the resurrection of Christ.
Whole books have been written on these topics. This is of necessity a brief summary. I encourage you to study so that you can explain these arguments in more detail where it is needed.
The above borrows heavily from On Guard by Williams Lane Craig.