How do we know when to separate Jesus's specific 
instruction to a disciple from His general instruction to everyone? 

He told the disciples to go out and perform miracles. 
Should Christians also do this?
    Context is the best way of determining if an instruction is general or specific. Who is the speaker talking to? To whom does he say the instruction is relevant? When Jesus is delivering a lesson on the necessary qualities that a kingdom citizen must possess (such as in the Sermon on the Mount), His instruction is for all who would be a part of His Kingdom. In regard to miracles, however, He delivered no such general instruction. In fact, Jesus informed the apostles in private that they would perform miracles as a part of a PROMISE, not a command. Jesus COMMANDED His disciples to go into the world to preach the gospel and baptize those who would believe. The signs that accompanied their ministry were marks of authenticity—these abilities were promised to them as a sign that they were messengers sent from God and that their message was indeed God’s will. So, their primary mission was never to “go out into the world and perform miracles,” but to go out into the world and preach the gospel to every creature. The gifts of the Spirit were a PROMISE, not a COMMAND—receiving power from on high was something they could not themselves command or control, thus, how could it be expected of them?
MATTHEW 28:19 "Go therefore and make disciples of all the nations, baptizing them in the name of the Father and the Son and the Holy Spirit,
 20 teaching them to observe all that I commanded you; and lo, I am with you always, even to the end of the age."
MARK 16:15 And He said to them, "Go into all the world and preach the gospel to all creation.
 16 "He who has believed and has been baptized shall be saved; but he who has disbelieved shall be condemned.
 17 "And these signs will accompany those who have believed: in My name they will cast out demons, they will speak with new tongues;
 18 they will pick up serpents, and if they drink any deadly poison, it shall not hurt them; they will lay hands on the sick, and they will recover."
    Signs and miracles were the means by which the Word was confirmed and established—but it would only be temporary, and would mark the end of such things. This was a matter of prophecy:
ZECHARIAH 13:1 "In that day a fountain will be opened for the house of David and for the inhabitants of Jerusalem, for sin and for impurity.
 2  "And it will come about in that day," declares the Lord of hosts, "that I will cut off the names of the idols from the land, and they will no longer be remembered; and I will also remove the prophets and the unclean spirit from the land.
    Verse 1 points to the preaching of the gospel for the first time in Jerusalem in Acts 2—during that time (the spreading of the gospel) the ranks of pagan gods of the ancient world would be forgotten (Where are Zeus, Athena, & co. now?) and prophets would be removed from the land.

    Knowledge and prophecy granted by the Spirit served as a “jump start” to a people who did not have a written New Testament—they had the apostles themselves, preaching and teaching in person. The completion of knowledge, God’s revelation, had not yet been realized. So, for the time being, this knowledge was handed down directly and confirmed by various signs. Messengers of God have always operated this way. Consider the Old Testament prophets--we remember them for the great miracles and signs God performed through them, but with every spectacle there was a MORAL, a MESSAGE, a WARNING. The signs accompanied these words to authenticate their origin as divine. So, to the first churches, even signs from the Holy Spirit were passed down from the apostles, by the laying on of their hands (Acts 8:17-18). With these gifts came instructions from the apostles on the proper administration of them (see 1 Cor 12-14). BUT along with that instruction came a clarification of their purpose—to establish the truth, which brings forth fruits of faith, hope, and love. These things would last, but the various miraculous proofs would not—they were temporary, to establish God’s new covenant. Paul was very clear on this.

1CORINTHIANS 13:8 Love never fails; but if there are gifts of prophecy, they will be done away; if there are tongues, they will cease; if there is knowledge, it will be done away.
 9 For we know in part, and we prophesy in part;
 10 but when the perfect comes, the partial will be done away.
    "Perfect" and "partial" of what? What's under consideration? KNOWLEDGE (v.9). When all knowledge is received and confirmed, there would no longer be a need to confirm it further. Signed, sealed, delivered. God had in mind a NEW way of communicating His will:
HEBREWS 1:1 God, after He spoke long ago to the fathers in the prophets in many portions and in many ways,
 2 in these last days has spoken to us in His Son, whom He appointed heir of all things, through whom also He made the world.
    God’s will today is passed down through the word of Christ, which is the GOSPEL:
COLOSSIANS 3:16 Let the word of Christ richly dwell within you, with all wisdom teaching and admonishing one another with psalms and hymns and spiritual songs, singing with thankfulness in your hearts to God.
    Miraculous gifts and prophecy do not exist today simply because there is no longer any need for them. The Word is established, the gospel is ours.
 

- Close-