Samuel Bolton writes,

The ceremonial law was an appendix to the first table of the moral law. It was an ordinance containing precepts of worship for the Jews when they were in their infancy…As for the judicial law, which was an appendix to the second table, it was an ordinance containing precepts concerning the government of the people in things civil…’ (The True Bounds of Christian Freedom, p. 56).

Taking this understanding of the ceremonial and civil laws as appendixes to the 10 Commandments, and taking Jesus’ declaration that the summary of the Law is ‘love God and love your neighbor’, we might diagram the Law in this way:

There are a couple of things about this diagram that need to be clarified. First, the fifth commandment is included in the first table of the law as pertaining to the honoring of authority (God’s authority being supreme). This is debatable, but not necessarily important for the current discussion. Second, the cleanliness law (purity laws dealing with the clean/unclean distinction) are set in the middle between ceremonial and civil law because cleanliness laws often pertained to both. Remember that the priests served not only as officials of worship (ceremonial) but also as health officials (civil) in some respects.

This paradigm (summary of the 10 Commandments>the 10 Commandments>the appendixes to the 10 Commandments) is a helpful grid through which we may pass any law as we determine its continuing validity. But before we get to that in detail we need to discuss the fulfillment of the Law in Christ. The teaching of Jesus Christ in the New Testament makes it abundantly clear that the moral essence of the law (the summary of the 10 Commandments and the 10 Commandments themselves) remain intact (cf. Mat. 5:17-18, 19:17-19, 22:37-40). Yet, while the moral essence of the Law remains, it is clear from the New Testament that in other areas there has been a broad change.

These changes all relate to the fulfillment of the appendixes of the law (see diagram above) and the laws relating to cleanness and uncleanness. In other words the moral core of the Law remains while the external, exact forms of keeping the Law are altered under the administration of the New Covenant. Relating this to the ceremonial and civil law this means that the external forms of worship and government have been drastically altered under the New Covenant reign of Christ. Here is a brief example:

• Leviticus 17:3 If any one of the house of Israel kills an ox or a lamb or a goat in the camp, or kills it outside the camp, 4 and does not bring it to the entrance of the tent of meeting to offer it as a gift to the LORD in front of the tabernacle of the LORD, bloodguilt shall be imputed to that man. He has shed blood, and that man shall be cut off from among his people.

•  John 4:21 Jesus said to her, “Woman, believe me, the hour is coming when neither on this mountain nor in Jerusalem will you worship the Father. 22 You worship what you do not know; we worship what we know, for salvation is from the Jews. 23 But the hour is coming, and is now here, when the true worshipers will worship the Father in spirit and truth, for the Father is seeking such people to worship him.

This law has obviously changed, for we no longer bring offerings to an earthly tabernacle, Christ being the fulfillment (anti-type) of the tabernacle (cf.Mat. 1:23;  John 1:14, 2:19; 1 Cor. 3:16ff., Eph. 2:21, Rev. 21:22, etc).

As for the laws of cleanness and uncleanness it appears that the New Testament teaching on the subject is that those laws have been entirely fulfilled by the work of Christ, as he takes all uncleanness upon himself, offering his own cleanness to those who are united to him by faith:

• John 13:10 Jesus said to him, “The one who has bathed does not need to wash, except for his feet, but is completely clean. And you are clean, but not every one of you.” 11 For he knew who was to betray him; that was why he said, “Not all of you are clean.”
• Mark 7:18 And he said to them, “Then are you also without understanding? Do you not see that whatever goes into a person from outside cannot defile him, 19 since it enters not his heart but his stomach, and is expelled?” ( Thus he declared all foods clean.)
• Ezekiel 36:25 I will sprinkle clean water on you, and you shall be clean from all your uncleannesses, and from all your idols I will cleanse you.
•  Acts 10:9 ¶ The next day, as they were on their journey and approaching the city, Peter went up on the housetop about the sixth hour to pray. 10 And he became hungry and wanted something to eat, but while they were preparing it, he fell into a trance 11 and saw the heavens opened and something like a great sheet descending, being let down by its four corners upon the earth. 12 In it were all kinds of animals and reptiles and birds of the air. 13 And there came a voice to him: “Rise, Peter; kill and eat.” 14 But Peter said, “By no means, Lord; for I have never eaten anything that is common or unclean.” 15 And the voice came to him again a second time, “What God has made clean, do not call common.”
• Acts 11:9 But the voice answered a second time from heaven, ‘What God has made clean, do not call common.’ 10 This happened three times, and all was drawn up again into heaven. 11 And behold, at that very moment three men arrived at the house in which we were, sent to me from Caesarea. 12 And the Spirit told me to go with them, making no distinction. These six brothers also accompanied me, and we entered the man’s house.
• 1 Corinthians 7:14 For the unbelieving husband is made holy because of his wife, and the unbelieving wife is made holy because of her husband. Otherwise your children would be unclean, but as it is, they are holy.
• Romans 14:14 I know and am persuaded in the Lord Jesus that nothing is unclean in itself, but it is unclean for anyone who thinks it unclean.
• Hebrews 9:13 For if the sprinkling of defiled persons with the blood of goats and bulls and with the ashes of a heifer sanctifies for the purification of the flesh, 14 how much more will the blood of Christ, who through the eternal Spirit offered himself without blemish to God, purify our conscience from dead works to serve the living God.
• Titus 1:15 To the pure, all things are pure, but to the defiled and unbelieving, nothing is pure; but both their minds and their consciences are defiled.
• Galatians 3:13 Christ redeemed us from the curse of the law by becoming a curse for us- for it is written, “Cursed is everyone who is hanged on a tree”-

In summary of what we’ve said so far, the moral essence of the law is binding (summary of the 10 Commandments and 10 commandments), the appendixes to the moral law (ceremonial and civil) must be evaluated in light of whether or not a particular law has been fulfilled by Christ or altered in its New Covenant application, and the Clean/Unclean Laws have all been fulfilled in Christ. That means that it is very easy to deal with straight-forward moral commands and laws dealing with cleanness and uncleanness. The former are still in force the latter are all fulfilled. The difficulty then is in dealing with those tricky appendixes. This is where we can get into trouble as interpreters, but this is also where our interpretation grid comes in handy.

Since the ceremonial and civil laws are basically appendixes to the 10 Commandments, and the 10 Commandments are summarized further as Love God, Love Neighbor, we should attempt to take those ceremonial and civil laws and locate them in the 10 Commandments and its summary. This will boil the precepts down to their moral essence. From there we can ask whether or not the essence of the command is fulfilled in Christ and determine if the individual laws have any modern application for us as Christians.

Let’s take one example. I’ve had to deal with this passage because some have interpreted it simply to mean that a woman should not wear pants:

• Deuteronomy 22:5 ¶ The woman shall not wear that which pertaineth unto a man, neither shall a man put on a woman’s garment: for all that do so are abomination unto the LORD thy God.

Using our grid, we need to locate this command in our grid. First, we know it’s not a cleanliness law. Second, then we can ask, ‘what part of the 10 Commandments is this law applying?’ The only law that makes sense is the 9th commandment (‘You shall not bear false witness’) because the general issue is deception – pretending to be something that you are not (i.e. a man looking like a woman, a woman looking like a man). This is therefore an issue of loving your neighbor, and the moral force of it is still relevant. How then can we honor this commandment? Some would say it is as simply as ‘a woman shouldn’t wear pants.’ But this is a very strict application of a rather broad rule. The moral force of the commandment is basically that a woman should not appear to be a man, or try to look like a man, and vice versa for men. Drag queens are breaking the 9th Commandment.

If I were to preach Deuteronomy 22:5, this should be the thrust of my application – don’t try to look like someone of the opposite sex for this is deceptive, untrue, and a violation of the 9th Commandment. The good news is that while the moral essence of the law is still in force, Christ has paid the price for our breaking of the 9th Commandment as offers forgiveness through penitent faith.

Another good example of how this grid works pertains to the gleaning laws of the Old Testament. As a part of the appendix to the civil law they relate back to the 8th Commandment (‘You shall not steal’). Those who refused to leave the crops in the corners of their fields for gleaners were taking what God had declared not to belong to them and, thus, in essence, stealing. And at the back of that stealing is the moral issue of coveting – they wanted what was not legally theirs (i.e. coveted) and so they stole it. The result of this is that they were not loving their neighbors. The moral force of such laws are still binding despite external changes – we should honor the poor and use our money to do good.

• Matthew 5:42 Give to the one who begs from you, and do not refuse the one who would borrow from you.

So, how can you interpret Levitical Law as a Christian?

1. If it is a cleanliness law it is fulfilled in Christ.

2. If it is a strictly moral law, relating to the 10 Commandments or the summary of the 10 Commandments, it is still in force.

3. If it is a ceremonial or civil law it must be examined in the light of New Testament teaching and then, if it is not explicitly fulfilled in the New Testament, it must be related back to the moral law to find its proper contemporary application.

In all these areas the Law is meant to point us to our need of Christ, but for the Christian, having discovered that need, and believed upon him, we will find in the Levitical Law wise and impactful ways of applying the moral law to our current situations. Look at it this way – the individual levitical laws give us angles from which to approach the 10 Commandments, and therefore angles from which we can apply them both to the unbeliever in need of justification and to the believer striving for sanctification.

Update: 8/27/14
I found a great quote (HERE)(about theonomy) that summarizes Bolton’s view well:

This constitutes an approach to the nature of the civil law very different from Calvin and the rest of the Reformed tradition, which sees the civil law as God’s application of his eternal standards to the particular exigencies of his people.

“God’s application of his eternal standards to the particular exigencies of his people” is another way of calling the civil (and ceremonial) law ‘appendixes’ to the moral law. This is precisely how we must view the law today: it is to be applied to the particular exigencies of God’s people under the administration of the New Covenant.