By successful, I don't mean "rich" or "educated" (the two success criteria of the western world) I mean successful by the only standard that matters - parenting that honours God.
God has given his people rich resources for parenting. There are numerous Scriptures that talk directly about parenting. There is the example of God the Father towards his only begotten Son. There is the example of God the Father towards us his adopted children, and there is the example in the church of successful parents passing on their godly experience. Add this collective Biblical wisdom together, and you end up with these six steps (at least)....
Love your kids unconditionally.
Nothing more resembles divine love than its enduring nature, the compassion of God never fails (Lamentations 3:32). God the Father told God his Son on at least two occasions (his baptism and transfiguration) that he loved him. Love your kids no matter what, and tell them you do.
Discipline your kids wisely.
It is very possible, according to the apostle Paul for discipline (and for general parenting for that matter) to result in angry kids (Ephesians 6:4 and Colossians 3:21). Perhaps the parent has failed to distinguish between childish irresponsibility (which does not need discipline, but needs patient instruction) and willful disobedience which does need discipline: they end up shouting at the children for everything - that'll get 'em mad. Perhaps the parent is hypocritical, expecting one thing from the child but doing another thing themselves. Perhaps the parent is too harsh. Perhaps overprotective, perhaps showing favoritism, perhaps inconsistent in discipline, perhaps negligent. All of these faults will result in anger in the child, not the correction of bad behaviour.
Affirm the positively.
Sometimes a parent has to do so much correcting that it seems as if they are being wholly negative all the time. At these seasons catch them doing something good and commend them for it. There is always something good to find. God the Father said he was "well pleased" with his Son.
Give them practical guidance about life.
The first chapters of Proverbs are full of rich instruction for parents of teens. Here Solomon takes his son(s) aside and lovingly warns them about violent men and loose women. It isn't only when they are children they need instruction, they need it when they are teens - and beyond.
Nurture them spiritually.
"In the nurture and admonition of the Lord" says Paul in Ephesians 6:4. Impress the word on your children, urges Moses in Deuteronomy 6:4-7. In both formal and informal ways, instruct them in spiritual matters. Remember on the last day you and not the church will be held to account.
Pray for them continually.
It's obvious but all too often neglected. I grew up in a family of eight. By the grace of God all six children were converted. And I believe to a large extent, under God, this is due to the godly example and the prayers of my parents.
On the 8th August 1979, when my mother was 58, she wrote this note about the day:
"This is my 58th birthday. It has been a happy one. It was not without weeping though as this morning I pleaded with God to turn Dianne (a backslidden daughter at that time) to Himself and remove all obstacles from her life… I prayed for all eight of us … that he may be glorified…"