In trying to understand Old Testament salvation, we have both the advantage and the disadvantage of having the New Testament. The New Testament is an advantage because we have some interpretive statements as to the purpose and limitations of the law and ways in which God dealt with Israel at this time. However, the New Testament works to our disadvantage because we will find it all but impossible to approach the Old Testament teachings without imposing our New Testament understanding on it. Therefore, we tend to read New Testament truths back into the Old Testament. The goal is to find a proper balance between the two.
I do not have a detailed plan of salvation to give that strictly applies to Old Testament saints. I do not even feel that it is critical for us today to understand in full detail the way they came to God. However, I will gladly give several of the biblical guidelines that will help keep us in safe territory.
First, the law in and of itself did not then and cannot today be a source of eternal life. The law provided two ways for man to approach God through his own works: by obedience to the commandments (Exodus 24:1-8; Leviticus 18:5; Deuteronomy 27:26) and by the making of sacrifices (Leviticus 1:1-4; 4:27-35). But neither of these gave eternal life. Obedience to the commandments could not save man because no man could keep all the commandments (Ecclesiastes 7:20; Romans 3:19-20; 12-14; 8:3; Galatians 2:16; 3:10-12, 21-22; Hebrews 7:18-19). The making of sacrifices could not save man because the blood of animals could not put away sin. We can see this both in Old Testament teaching (Psalm 51:16; Isaiah 1:11; Hosea 6:6) and in New Testament teaching (Hebrews 9:8-10, 10:1-4, 11). No man has ever been saved by keeping the law.
Second, even under the law, men came to God ultimately by faith. Even though their faith might be expressed in works (as ours should be), it was still faith that got God's attention. Hebrews 11 is often called the faith chapter in the Bible. The passage gives a list of men and women of the Old Testament who were known for their faith. Several of these lived under the law. In Hebrews 11:13 we read this general statement: "These all died in faith, not having received the promises, but having seen them afar off, and were persuaded of them, and embraced them, and confessed that they were strangers and pilgrims on the earth." Evidently, the key that united all of these men and women was their faith and the fact that they died in faith.
But what did their faith do for them? Well, it seems to have imputed unto them (at least in the legal sense) the righteousness of God. I realize that the proof text often used in the New Testament refers to the faith of Abraham, a man who lived long before the giving of the law (Genesis 15:1-6; Romans 4:1-5; Galatians 3:6; James 2:23). But consider the following passage from Romans.
Romans 3:21 But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets; 22 Even the righteousness of God which is by faith of Jesus Christ unto all and upon all them that believe: for there is no difference:
This passage states that the righteousness of God without the law was witnessed by the law and prophets. This certainly refers to the imputed righteousness of God on those who believe. Certainly, the Old Testament saints did not have to understand the payment that Christ would make for them on the cross. Neither am I claiming that Old Testament salvation is equal in every respect to that of New Testament saints. It is not. Their sins were not totally cleansed as ours are. They did not have the indwelling of the Spirit as a seal to their faith. They probably did not have the assurance of eternal life, at least not in the way we have it today. However, they accepted the word of the Lord, trusted in Him, and had His righteousness imputed to them because of their faith. This held their judgment in reserve until the coming of Christ and the application of His shed blood "for the redemption of the transgressions that were under the first testament" (Hebrews 9:15).
I realize that I have not answered all the questions you may have. I am sure that I cannot answer many questions that could be asked. This is a complex subject. Unfortunately, believers are now using Old Testament salvation as another cause of division. This is true even among those who agree on the plan of salvation for today. This is sad. But I hope that my comments will at least be a help to you in your study of God's word.