First cause - that unless something is caused it does not exist. Everything in our universe is caused. Something therefore must have been caused it. Whatever that cause was, that we may call God, even if we have no idea of who God is!
First movement - that unless something is moved by forces acting upon it, it does not move. Everything in the universe is in motion. Whatever it was that activated the whole lot, that we my call God.
Contingency - the reverse of the first cause argument. If a thing might not existed, it is called contingent. You are a contingent being because you might never have existed? Of course. It is therefore contingent. It must exist for a reason, a cause. Is it possible that the entire cosmos with all its universes might never existed? We suppose so - therefore the whole lot is contingent. Thus, there must have been something which caused it all to be, and that we call God.
Necessary being - this is also called Ontological argument because it involves a logical play on words. God must be 'necessary' because a scale of values exist. Some things are bad, some are better, and at the top there is that which is best. Can there be "two" bests"? No, not by defintion of what we mean by best. That which is at the top of our values we may call God. And He must exist because that which does not exist cannot be the best; if it doesn't exist it cannot be the best; if it doesn't exist it cannot be regarded as supremely anything. Therefore if there is a supreme of the scale of values, it, or He, must exist.
Design - this is also called the Teleological argument because it looks forward to an end, aim or goal. The universe in every aspect of its laws and their physical manifestations shows order and pattern - other words, design. They do not appear to have evolved, they have evolved to a pattern, and seem to be moving towards an ultimate goal, even if we do not know what that goal is.
From What every Christian should know about Islam by Ruqaiyyah waris maqsood.