There are many analogies and different tools I've used to explain the gospel story - or parts of the gospel - to unbelievers over the years. Inspired by a fellow Christian writer, I would like to share some of the analogies and tools I have found most useful.
1) The Light and the Dark - If heaven is perfect, as a place where the very presence of God resides, then how can something that is imperfect enter in? Does that not make it imperfect? Here is the analogy.
If God is truly perfect, then he could be analogous to pure light. Sin, being a blemish or a wrong, could be analogous to darkness. Now the only difference, is sin is like a stain on the soul - a darkness that cannot come out so easily. Now if, let us say, someone whose soul was still stained with sin entered God's presence, what would happen? Well, what happens to darkness when the light is turned on? It disappears. So what would happen if darkness entered the presence of pure light - nothing to shadow or stand in the way? It would utterly disappear completely. So what would happen to a soul stained with darkness (sin) if it happened to enter the presence of God (pure light)? It would be utterly destroyed.
Conclusions - God doesn't let just anyone enter heaven, you cannot enter upon your own merit (for no one is without some sin), and since personal merit doesn't work, only one solution has been presented. Jesus' sacrifice, taking your sin upon himself - is likened to the use of bleach on the soul. It wipes it clean - if you confess with your mouth that Jesus is Lord and believe in your heart God rose him from the dead, you WILL be saved. --- and there is NO OTHER WAY!
This answers - in part or in full - questions such as - why won't everyone be saved? why is Jesus the only way? why do I need to be saved? why won't God accept everyone? etc.
2) The wedding and the dirt - What does salvation look like?
No analogy is perfect, but one visual I have used is of a kingdom whose prince is getting married. All the townsfolk and surrounding area has been invited to the wedding - but mores dictate a certain decorum be present for anyone to attend the wedding (i.e. if you come unbathed and in raggedy clothing, you won't be permitted entrance). Your family traveled almost all day to attend this wedding, and privileged or not, your family can't afford to head back home and expect to make it to the wedding on time. Your arrive at the castle with time to spare, and your parents leave you with a firm warning, "DON"T get dirty!" But like telling someone "Don't touch the red button!" what are you going to do? Well, you're going to "touch the red button!" You get dirty (doesn't really matter how dirty we're talking about here), and there's no time to head back for a change of clothes. You, regardless of your age, status, deeds, or affiliation, will not be permitted to come to the wedding. However, here's the craziness and beauty of the gospel story. The Prince comes and finds you and learns of your predicament. He gives you the clothes off his own back (so to speak), and allows you to enter and attend his wedding. This Prince thinks so much of you, a stranger and a peasant, that he is more than willing to inconvenience himself on his wedding day to attend to your problem, because you are so important to him that he wants you to attend his wedding. That's the beautiful picture of the Gospel. In your sin (large or small), that you cannot recompense on your own (for the penalty is death), Jesus died for you (gave you the shirt off his back) so that His righteousness will attributed to your account. And He did this by no deed of your own, but for His own pleasure. Because He wanted to - as a gift to you.
3) The 10 commandments tool - I'm a good person!
A long time ago I heard a traveling evangelist who would go through the 10 Commandments for people to express that no one stands up to "I'm a good person". Usually, he wouldn't go through all ten, just the big ones.
1] No other God before Him. Well, an idol is anything put in your life that is more important than God himself. So, if anything is more important, that's an Idol and it breaks the first commandment. - So I am an idolater.
2] Don't take the Lord's name in vain. Most people, when honest, would say they've said "Oh God!" or something similar in their lifetime. I know I have. - So I am a blasphemer.
3] Do not commit murder. Most people haven't murdered anyone, but Jesus said anyone who hates his brother (or anyone) breaks this commandment in his heart. - So I am a murderer.
4] Do not commit adultery. This one is slipping in our society, but let's say the person you're talking to hasn't committed the act. Well, Jesus said even looking at a woman (or man) with lust in your heart is the same a breaking this commandment. - So I am an adulterer.
5] Do not covet (i.e. do not steal). Most people would say they haven't stolen, but that usually means they haven't committed grand theft or big crimes - but have you ever stolen a cookie from the cookie jar? Or the answers from a neighboring student or friend? Stealing one thing, even a small, insignificant thing, still makes you a thief. - So I am a thief.
6] Do not give false testimony (i.e. don't lie). White lies, fibs, fabrications, exaggerations, manipulations, omissions - these are all different words for the same thing - a lie, and not telling the truth, even once, no matter how small the infraction, still makes you a liar. - So I am a liar.
Just six so far, I have just proven that I am a lying, thieving, blasphemous, Idolatrous, adulterating murderer. And I'm the Christian!
At this point, if it's not conceded that they are in the same boat as I, and that there is, in fact, a problem, and that a solution is needed, then... I'm not sure what to tell you!
Caveat - This tool is not to be used to beat someone over the head with. It is merely an exercise to show that however "good" a person he/she is, it's not good enough to enter heaven.
4) The painter and the star. - If there is a God, he must hate me!
If you were to pain the night sky, in all it's beauty and brilliance - how would you start? Well, a painter would start, of course, by pitching black -pitch black- over the entire canvass. (Pretty bleak, huh?) He would put down ALL the DARK colors before putting down the light colors that will eventually dazzle the audience in the starry night. If Dark is the bad times, and the light is the good times, then which is predominant in this picture? It would be the darkness. BUT, in light of the ENTIRE picture, what would most people say and what would most people notice? The brilliance and brightness of the starry night! Of the stars! Some of the most brilliant and awe inspiring pictures have the greatest contrasts.
Caveat - that is not to say that God must use the bad times to make the good times better, or that God has to use bad times to make good times, but simply that the good times are so good that it makes the bad worth surviving... (hopefully that makes sense)
5) The blacksmith and the metals. - The purpose of the Christian life is to become more and more like Jesus - To know and love God and to make his love known to others. - God loves us too much to leave us as we are.
Many analogies can go in here. In processing, naturally found gold is not pure. To purify it. They must do the same with silver. With silver, they melt it down - completely - scoop up the dross of the top, and what's left behind is pure silver. However, the best analogy of this kind, I believe, is of the blacksmith. To make anything - a horseshoe, a sword, a spoon, or whatever, the blacksmith must know exactly how long to keep the metal in the fire. If it's in there too long, it will melt away, and the blacksmith won't be able to mold it into anything. If it's not in there long enough, it will remain hard, and the blacksmith won't be able to mold it into anything either. He must keep it in the fire for JUST the right amount of time - not too firm, not too soft. Then he can hammer out the shape he so desires. We are lucky. We have the perfect Blacksmith. He knows just how long to keep us in the fire to mold us into the shape He desires us to be.
I may have forgotten some or missed some, but those are some of my favorites.