OT saints were saved the same as NT saints Faith alone in Christ alone. They looked forward to God's fulfillment of His promise in Gen 3:15 and to Abraham that he would send a Messiah.
The Holy Spirit came upon people in the OT, Saul, David, the prophets, but believers were not indwelt by the Holy Spirit until Pentecost. In John 9:39. The Spirit was given after Jesus was glorified