I think that the main way God used to lead people to himself was to use the people of Israel as an example, to show his glory, power and love through them, so that the surrounding peoples could see and accept that he is the only God.
One thing you could do, as a heathen of that time, was to convert and implant yourself in the state and people of Israel, just like we do today (though we are not referring to the state of Israel per se).
In the Old Testament, there are a number of people that were definitely people of God, although they were not Israelites. Four of them are Melchizedek, Jethro, Rahab and Ruth. Let's examine them, one by one:
Melchizedek was a priest of God and king in the city of Salem. Abra(ha)m was greeted and blessed by Melchizedek when they met. Melchizedek is mentioned in Genesis chapter 14. There is no mentioning of how Melchizedek had heard about God and there are many theories about this.
Jethro is introduced in Exodus 2:16, as a priest in the land of Midian. As far as I know, it is not explicitly stated that he was a priest of God, but in the 18th chapter, we can read that Jethro heard about what God had done for the people of Israel and praised him.
Rahab was a prostitute that lived in the city of Jericho. Before the siege, Joshua sent two spies to the city. For some reason they ended up in Rahab's house and she protected them from their enemies. She believed in God, for she had heard about what God had done for the people of Israel and put her faith in him. She asked the spies to protect her and her family and not let them perish with the rest of the people of Jericho and so they became a part of the Israelites, and Rahab became an ancestor to Jesus, our Savior.
Ruth was married to one of the sons of Naomi, a woman of the Israelites. She is mentioned in the book of Ruth. I think it is fair to assume that she heard about God from her mother- and father-in-law, and her husband. Later, she followed her mother-in-law back to the land of Israel and became a part of the Israelites, and ancestor to Jesus, our Savior, just like Rahab.