Biblical Case:

Matthew 28:18-20 (ESV)
18 ““And Jesus came and said to them, “All authority in heaven and on earth has been given to me.
19 Go therefore and make disciples of all nations, (1) baptizing them in (into) the name of the Father and of the Son and of the Holy Spirit,
20 (2) teaching them to observe all that I have commanded you. And behold, I am with you always, to the end of the age.””

1. Baptizing (into) the name.... It’s more than a water ceremony; it is a Spiritual Transplant into The Resurrected Race.
2. To observe here is literally to “watch or guard” the commands of the King

Jesus discipled generally and specifically.

In the case of Peter.
1) He is generally called to repent and to live out the Sermon on the Mount.
2) He is specifically discipled prophetically into his destiny:

John 1:41-42 (ESV)
41 “He first found his own brother Simon and said to him, “We have found the Messiah” (which means Christ).
42 He brought him to Jesus. Jesus looked at him and said, “You are Simon the son of John. You shall be called Cephas” (which means Peter).”

Matthew 16:17-19 (ESV)
17 “And Jesus answered him, “Blessed are you, Simon Bar-Jonah! For flesh and blood has not revealed this to you, but my Father who is in heaven.
18 And I tell you, you are Peter, and on this rock I will build my church, and the gates of hell shall not prevail against it.
19 I will give you the keys of the kingdom of heaven, and whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven.””

Paul disciples Timothy:
1) generally, by teaching him as he would teach all about faith Christ and holiness, etc.
2) but he also specifically discipled him prophetically:

1 Timothy 1:18 (ESV)
18 “This charge I entrust to you, Timothy, my child, in accordance with the prophecies previously made about you, that by them you may wage the good warfare,”