There are two way to talk to Jews and Muslims about Christian God. One is to start from the presumption that their God is our God the Father, and then go on convincing them that Jesus the Son is God also. It is not hard to get as far as agreeing that Jesus was an exceptional man, -- the Koran, after all devotes several heart-felt chapters to Him, and modern Jews readily accept, and claim as their own, Christian moral teaching. To get to divinity of Christ from that starting point is near impossible, because any logical argument you might make ends up with "Yeah, great man..."
Then you have to describe the Holy Spirit as a third divine person, and that is met with total incomprehension.
But the premise is wrong. It is, in fact not a Christian premise. This is why it does not work practically.
Here's a fulcrum question. Was God of Abraham one in three persons?
Well, there was no Jesus around. Sure there was Melchizedek and the Ram -- not Lamb -- of God that substituted for Isaac, but these are types, not hard teaching. Yet the Iconographer knew enough to depict the Trinity in the persons of three angels at Abraham's table.
The insight of this icon is that whenever one thinks of God, one thinks of Triune God. When an Aborogene puts a shriveled lizard in his pipe and smokes it to find out about God (I assume that's what they do), he is seeking the Triune God, not the Father in isolaton from the Son and the Holy Ghost.
There was a discussion here whether Allah means God. Well, it happens to mean so in Arabic, just as much as ha-El, or more often, Elohim (plural!), mean God in Hebrew (YWHW is His proper name, not the ontological name). But here's what Allah doesn't mean, it doesn't mean "the Father".
So what does it do to my and your discussions with Jews, Atheists and Muslims?
We do not have to convince them that they worship the right God Who has Trinity Partners. This is incorrect Christian theology and so it does not convince. It only convinces them that we are polytheists.
The truth is that Christ "through Whom all things were made" was there from the beginning. He was offering the Eucharist to Abraham, and He was blessing Abraham's table. The Holy Spirit was there hovering over the waters before there were waters and breaking Jacob's leg. The God the Muslims and the Jews worship is our God allright, but they do not see Him fully, so they don't worship Him right. He has no partners, He has persons inside of Him. As He always had.