How did Abraham know that it was the one true God who was calling him if he lived in a society of paganaism and idolotry?

A very good question! For any reasonable argument, it seems Abraham really shouldn't have believed God. I mean, in Genesis 11, Abram (as his name formerly was) is introduced by his family lineage... and suddenly God is in the picture telling Abram he's going to go on this very long journey far from home. Perhaps there's more to this story than we initially see, but ultimately Abram just trusted God. Perhaps God's directness with Abram made a difference. The other "gods" would "provide" for their people by allowing the sun to rise each morning and by bringing the seasonal rains so a good crop could be produced. But here, with God, we see that he spoke with Abram. He told him to leave his land and take his family on the whim of "being made a great nation". And Abram did. For about 30 years he followed God wherever He directed and this was a long, perilous journey, something that can't be seen through Scripture alone. What's more, Abram followed God for about 30 years before ever seeing any real fulfillment of the Lord's promises. Even though those years were riddled with doubt and questioning, Abram stuck with it. And God SO blessed him, and so blessed him in ways that Abram couldn't even understand. Abram followed God understanding that he would be made a "great nation". As far as he understand and could imagine, he would have sons and those sons would have sons. And that did in fact happen. But God gave him so much more. Through Abraham every nation was blessed, because from Abraham's body a seed was carried through his sons and grandsons and great grandsons, including a trail of many great people, such as King David, and ultimately the Messiah, Jesus Christ, through whom the salvation of all people is found. Because of Abraham's great faith in the Lord, all people who have this same faith are "sons and daughters" of Abraham. So, initially, Abram had no real reason to believe God. Perhaps it was because God came close. He was personal. He spoke directly to him and told him where he wanted him to go and what he could expect out of it. And Abram was saved through this faith. We find ourselves in Genesis 15. Here, about 30 years after choosing to follow God, Abram confronts God. He tells him, you promised me a child… and look here, no child. Can you even do the things you say? I should just give up… no child of mine will receive my inheritance. A servant of my household will receive my inheritance. So God takes him out, and gives him a little reality check. "Do you see what I have made with my own hands?" God asks. Look at the stars, just TRY to count them. Can you? Do you see how big I am, and how small you are?" And yet, God choose Abram. Despite being so big, God singled him out with a divine plan for his life, and a wonderful fulfillment of his plan for all the earth. Again, God promises to give Abram a son. Not just a son, but a whole line of sons, ultimately Jesus, who will save all those who believe in him. And Abram believed God. Abram believed in Jesus. And quite simply, "Abram believed the LORD, and He credited it to him as righteousness" Genesis 15:6. Abram was saved through his faith. No more just going along, maybe God will do what He says, maybe He won't. Abram surrenders. And God makes a beautiful covenant with him. One that illustrates, not only will God prevail His promise, but when Abram and all of humanity fail their promise to honor and love God, God will die for them. He will make everything ok. So Abraham chose faith in God, and God blessed him. He gave him continued assurance, fulfillment of promises, and a "peace that passes understanding". This is what Christian's have in God. Faith, by any account is not reasonable. It is certain, but not reasonable by any measurable standard.