A closed sign is an excellent analogy to explain the distinction between the Old and New Testaments. A closed sign always means what it says. "Sorry, we're closed" does not leave a lot of room for interpretation. However, the direction in which the sign is facing does.
When a closed sign is facing the entrance, and especially if the door is locked, it is intended to tell people not to enter. By contrast, when the sign is turned around, it still says "Sorry, we're closed", yet the words "Come in, we're open" are now facing the entrance, allowing potential customers to enter.
The Old Testament still means the same thing today as it did 2,000 years ago. It hasn't suddenly changed meaning just because Jesus showed up. However, the Bible does tell us that Jesus fulfilled the law (Matthew 5:17), and that because of this, we are no longer under it (Romans 6:14; Galatians 3:24-25). The closed sign, so to speak, is facing the other direction.
There are several other analogies we could draw here. For example, the distinction between moral and covenantal law could be shown by the definition of trespassing. Trespassing is defined in the law as "going beyond the permissions given". When the sign is open, you have permission to enter the premises. You do not, however, have permission to break down the door, cuss out the staff, walk behind the counter and alter the music playlist, things like that. Similarly, the Old Testament does describe some laws that were not revoked, but rather renewed. Blasphemy, murder, rape (which is actually akin to murder), kidnapping, adultery, slander, homosexuality, these are all things which are condemned in the Old Testament, and yet the New Testament renews them. By contrast, the New Testament clearly tells us that whatever you believe you can eat, you can eat (e.g. Romans 14). Therefore, Old Testament dietary laws have passed away.
There is also the concept of authority. Not everyone has to obey the closed sign. The staff, and especially the manager, are all permitted to disregard the closed sign, and can sometimes grant others that authority, either in certain situations, or under all circumstances. For example, the sign in the header image is actually at my favourite local cafe. Normally, I am just a customer, and must wait outside until opening time. I am certainly not permitted to enter the side door. However, one morning, one of the staff noticed me on my way to wait outside, and invited me to enter the side door to get out of the cold and rain. Because I was given explicit permission by an authoritative member of staff, it was not trespassing for me to defy the closed sign.
Similarly, God is not bound to His own laws. He can break, alter or suspend them at any given time. He can also permit/command others to do so. This is actually critical for the New Testament. If God could not alter the law, the moment God forbade pork, it would have been impossible for Him to later tell Peter "rise, Peter, kill and eat". Of course, by His very nature, God is not arbitrary. He won't suddenly declare, for example, that there is to be an annual purge, allowing 12 hours of pure anarchy. He is loving and consistent. However, it is illogical to look at any action of God, such as the flood of Noah's day, and say "that was evil, God has no right to kill". Of course God has the right to kill, just as a manager has the right to disregard his own closed sign.
The closed sign analogy, of course, is not perfect. No analogy ever will be. However, it does help us to understand Biblical morality in a way most people fail to do. It is illogical, for example, for an atheist to say "Christians are hypocrites because they eat bacon", or "the Bible is full of contradictions", then compare two verses from different sides of the New Covenant. It is also illogical for an atheist to say "God is evil because...". All of these arguments, and more, are solved by an adequate understanding of the context.
Ultimately, the entire Bible gives us one message. Man was designed to relate to God as obedient children. When we fail in that duty, we forfeit this relationship and earn God's wrath. However, God has no intention of delivering that wrath. Rather than punish us immediately, as we deserve, God instead sent Jesus to live as a man and die on the cross. Through the death of Christ, God can now legally forgive us for our sins. All we have to do is confess Jesus as Lord and believe He rose from the dead.