How were Old Testament believers saved?

Old Testament believers were saved by virtue of their faith. They held the position of saved people, as we would call it today, through believing. Their righteousness and standing before God rested on faith, not works or ritual, and they were counted among the redeemed awaiting resurrection.

Les explains that Old Testament believers were in their position as saved people by virtue of their faith. He notes this is how we would describe it today. They are saved by faith, and the believing element will be resurrected, while the rest go to shame and everlasting contempt. The wise shall shine as the brightness of the firmament, and those who turn many to righteousness as the stars forever and ever. This ties their salvation to faith, not to any other means, and connects them to the resurrection hope.

Daniel 12:2

And many of them that sleep in the dust of the earth shall awake, some to everlasting life, and some to shame and everlasting contempt.

Were Old Testament believers saved the same way believers are saved today?

Old Testament believers were saved by faith, just as believers are saved today. The context describes them as saved people in their position before God by virtue of their faith. Their standing as saved individuals rested on faith, which is the same basis for salvation today.