This is the best explanation of the duality of man I have found. in the second part it assumes that the soul and spirit are the same entity.

quoted from http://www.ligonier.org/learn/devotionals/duality-man/

The Duality of Man

“And many of those who sleep in the dust of the earth shall awake, some to everlasting life, and some to shame and everlasting contempt” (Dan. 12:2).

When theologians explore what it means to be in the image of God after the fall, typically there is a distinction made between the imago Dei in the narrow sense and the imago Dei in the wider sense. In the wider sense, we can say that after the fall we are still in the image of God because we still retain our humanity. Although sin has corrupted all of our physical, mental, and spiritual faculties, we still make use of them. Because we can still think, formulate plans, and the like, we retain the image of the Lord in the wider sense. However, in Adam we have lost the image of God in its narrower aspect. The imago Dei in this sense is conformitas — the ability to obey God. After the fall, man, of his own volition, can no longer conform to the Lord’s will.

Christianity confesses that God is Spirit and does not possess a physical body (John 4:24). The Lord’s moral attributes, such as faithfulness and intelligence, are not in any way dependent on physical corporeality, even though they were fully manifested in the life of Jesus. Similarly, these faculties remain present in us apart from the body. For example, we are still moral beings even if we happen to lose an arm and our bodies become incomplete. All of this is not to say that for human beings, the body is not essential to being made in the image of God. It is the unified body and soul that is made in His image (Gen. 1:26–27). Furthermore, if we hope to be righteous we must obey our Creator with our physical flesh. Though we can distinguish between body and soul, we cannot separate them. What we do to one affects the other. The false teachers John confronted in his first epistle may have believed what they did to the body was of no consequence as long as the soul was in order, but the Bible knows of no such view.

We are the image of God physically, not in the sense that God has a human body but in the sense that we can use our bodies as instruments of holiness. We must be careful not to think the body is inherently evil. It too is “good” (Gen. 1:31), and though presently marred by sin, it will be redeemed at the resurrection (Dan. 12:2). Coram Deo

The Bible teaches duality — man is composed of body and soul that exist together harmoniously. This is different from dualism — body and soul are opposed to one another. We must be careful to take care of our bodies by eating well, exercising, and such things, because how we care for ourselves reflects what we think about God’s image. Consider how you care for yourself and what you must do to be healthy and glorify God with your lifestyle.

The argument for the dual nature of man is based on Genesis 2:7.

And the Lord God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul. Genesis 2:7

This would imply dust of the ground (body) + breath of life (spirit) = a living soul. Both of the body and spirit must be present for there to be life at least for humans.

In death there is a separation from the spirit which returns to God and the dust which returns to the earth. Neither the spirit or body are conscious in death.

Then shall the dust return to the earth as it was: and the spirit shall return unto God who gave it. Ecclesiastes 12:7

The living know that they shall die: but the dead know not any thing, neither have they any more a reward; for the memory of them is forgotten. Also their love, and their hatred, and their envy, is now perished; neither have they any more a portion for ever in any thing that is done under the sun. Ecclesiastes 9:5,6

The spirit that returns to God seems individual. This would seem to indicate that the spirit contains what we are as individuals probably our memories and character.

And when Jesus had cried with a loud voice, he said, Father, into thy hands I commend my spirit: and having said thus, he gave up the ghost. Luke 23:46

In Hebrews 4:12 the emphasis is in the sharpness of God's word and how it can penetrate the inseparable. In this case the soul and spirit are inseparable because there is no soul without the spirit. Also there is no joint without the marrow.

Wayne Grudem's defense of dichotomism in his Systematic Theology, chapter 23 is particularly helpful in this regard. He lays out several kinds of biblical evidence, cleanly organizing the arguments made by previous Reformed theologians. His points are:

• Scripture uses soul and spirit interchangeably
  • "Soul" departs and "spirit" departs
  • Man is "body and soul" as well as "body and spirit"
  • "Soul" can sin and "spirit" can sin
• The actions of the soul are also the actions of the spirit, and vice versa

^{(All scripture cited is from the ESV unless otherwise noted)}

Scripture uses soul and spirit interchangeably

Grudem points to a number of passages that he argues are examples of the interchangeable use of soul and spirit. For example:

John 12:27: "Now is my soul troubled"
John 13:21: Jesus was troubled in his spirit

He sees Luke 1:46–47 as an example of Hebrew parallelism:

"My soul magnifies the Lord, and my spirit rejoices in God my Savior"

And those who have died are described as both spirits (Hebrews 12:23, 1 Peter 3:19) and souls (Revelation 6:9, 20:4).

He makes a simmilar argument for three main areas: the departing of soul and spirit at death, the formula "body and soul/spirit," and how both soul and spirit can sin.

Departure at death

A number of passages use "soul" to describe what departs when man dies:

Genesis 35:18: And as her soul was departing (for she was dying), she called his name Ben-oni
1 Kings 17:21 (NKJV): “O Lord my God, I pray, let this child’s soul come back to him.”
Isaiah 53:12: because he poured out his soul to death
Luke 12:20: 'Fool! This night your soul is required of you’

But elsewhere, "spirit" is used similarly:

Psalm 31:5: Into your hand I commit my spirit
Ecclesiastes 12:7: the dust returns to the earth as it was, and the spirit returns to God who gave it.
John 19:30: he bowed his head and gave up his spirit
Acts 7:59: "Lord Jesus, receive my spirit."

In response to the argument that these passages refer to different entities, Grudem notes that the Bible never says that a person's "soul and spirit" departed; always one or the other. Biblical writers don't seem concerned that one or the other might be left on earth with the body, suggesting that they are one and the same.

"Body and soul/spirit"

Grudem argues that biblical passages regularly refer to "body and soul" or "body and spirit" to describe the whole nature of man, not leaving out any parts. For example, Matthew 10:28:

And do not fear those who kill the body but cannot kill the soul. Rather fear him who can destroy both soul and body in hell.

The same thing occurs with spirit, for example, 1 Corinthians 5:5:

you are to deliver this man to Satan for the destruction of the flesh, so that his spirit may be saved in the day of the Lord.

Other passages along these lines include James 2:26, 1 Corinthians 7:34, and 2 Corinthians 7:1.

Both soul and spirit can sin

The sinfulness of the spirit is often denied by trichonomists, but Grudem points to scriptural evidence for the sinfulness of both soul and spirit. Regarding the soul, he points to 1 Peter 1:22 and Revelation 18:14, while passages indicating the sins of the spirit include 2 Corinthians 7:1:

let us cleanse ourselves from every defilement of body and spirit

Similarly, Deuteronomy 2:30 refers to the hardened spirit of the king of Heshbon, and Psalm 78:8 refers to the faithlessness of the spirits of the people of Israel. Other passages like Proverbs 16:2, Psalm 32:2, Psalm 51:10, and Proverbs 16:32 suggest that our spirits can be sinful.

Identical capabilities

Grudem finally argues that the soul and spirit are shown to have the same capabilities in the Bible. Trichonomists attempt to draw distinctions between the spirit's actions (such as worship and prayer) and the soul's actions (such as thinking, feeling, and deciding), but this distinction is not maintained by Scripture.

Feeling is described of the spirit in John 13:21 and Acts 17:16, the latter of which says:

Now while Paul was waiting for them at Athens, his spirit was provoked within him as he saw that the city was full of idols.

Thinking too is a function of the spirit in Mark 2:8, Romans 8:16, and especially 1 Corinthians 2:11:

For who knows a person's thoughts except the spirit of that person, which is in him?

On the other side of things, the soul is often said to worship God. Among many examples are Psalm 103:1, 146:1, and Luke 1:46, and the Bible teaches that souls pray and long for God (1 Samuel 1:15, Psalm 42:1–2, Psalm 119:20).

Grudem concludes:

Scripture does not seem to support any distinction between soul and spirit. There does not seem to be a satisfactory answer to the questions that we may address to a trichotomist, "What can the spirit do that the soul cannot do? What can the soul do that the spirit cannot do?"

Counterarguments

Grudem addresses a variety of trichonomist arguments, including that of Hebrews 4:12. Full explanation of his counterarguments is beyond the scope of this answer, but in brief:

• 1 Thessalonians 5:23, "may your whole spirit and soul and body be kept blameless": Grudem argues that this is best understood as a "piling up" of synonyms, similar to Matthew 22:37's heart, soul, and mind. Treating that passage and Mark 12:30 the same way would seem to indicate five or six parts of man.
• Hebrews 4:12, "piercing to the division of soul and of spirit": Soul is not separated from spirit here, says Grudem, but both are said to be penetrated and divided. For more on this, including other approaches, see How do proponents of the dual nature of man address Hebrews 4:12, “dividing soul and spirit”?

Summary

Grudem admits that arguments for trichotomism have "some force" but finds that:

the wide testimony of Scripture [shows] that the terms soul and spirit are frequently interchangeable and are in many cases synonymous.