Let me ask you a question: Is cannabis legal? Your answer will depend on where you live. Here in the UK, it is still illegal to smoke cannabis. By contrast, there are some regions that have either lifted the ban, or simply never had one in the first place.
The question as to whether or not cannabis is legal requires some form of legislative body. If there is no legislative body to pass a law against cannabis, cannabis can neither be illegal, as there is no law prohibiting it, nor legal, because there is no law at all. A person living in a region lacking such an authority is completely free to decide whether or not to smoke cannabis. They may even attempt to seek power, or someone else will. The ironic thing about Anarchy is that if there are no rules, there are no rules to prevent someone making rules.
Just as a legislative body is required for legal issues, a god of some form is required for moral issues. Furthermore, it cannot be a finite god. If it is a finite god, with both a beginning and an end, they hit the same problem. It wouldn't be that their authority is more legitimate than ours, but rather, they would just happen to have greater power.
If, however, we are talking about an infinite god, such as the Creator God of the Bible, things start to get more objective. First, we are talking about the rights of a Creator over His creation. If I make something (e.g. a plate), I have the right to decide the purpose of that plate, both before and during its existence. I can decide to make it a decorative plate, intended only for display. I can make it a plate for food. I can even make it just to destroy it. Whatever the purpose of the plate, I have full control over it as creator. Similarly, God has the absolute right to decide our purpose ahead of time, to give us commands during our lives, and to either sustain or destroy us. The only real legitimate limit to God's authority is... God's authority. He is bound to His own rules, which He will not break simply because it is not in His nature to do so.
Second, we're talking about the God who wrote natural law, too. Living beings are the only things in this universe that do not always obey God. This can be seen in miracles. For example, when Jesus and His disciples were caught in a storm, He told the storm to be quiet, and the storm was quiet. The laws God gives us are exactly as authoritative as the laws God gives nature. It just happens that He also gives us the physical ability to resist those commands.
If we ignore God's authority, morality becomes a made up concept, no stronger than a regular man made law. We can say "in my opinion, this is good" or "I believe this is evil", but in the end, it just becomes opinion. But most of us know this isn't the case. In fact, most of us recognise that there is an authority greater than the laws of our land. We can call out corruption and tyranny because it is corrupt and tyrannical. Might and right are two different things, and we know it. We are therefore faced with two consistent choices.
First, we can deny our moral instincts, claiming that even the greatest atrocities we can think of are, at best, merely undesirable to us. Slavery, Democide, Fascism, you name it, if there is no God, we have to acknowledge that our personal distaste for these things is just that: A personal distaste. The one who is "right" is the one with the biggest gun. Alternatively, we can acknowledge our moral instincts, but follow them through to the logical conclusion: These moral laws were given by a moral law giver.
In the case of the former, which I am sad to say I have seen some people do, there isn't really a lot that can be said to help you. I can try, however, and the way I like to do it is to highlight the difference between subjective laws and objective ones. Which side of the road does your country drive on? The UK and the U.S. drive on different sides. Neither one is correct. Compare that with laws pertaining to murder. Here, we recognise that it's a little more than just national preference. If the law says you can stab a man for looking at your wife wrong, that's a problem. And you know it. So, if you fall into the former category, maybe admit that morality isn't as subjective as you claim.
In the case of the latter, we have some uncomfortable questions to ask. Who is this moral law giver, what do they expect of me, and have I fulfilled those expectations?
Throughout history, the God of the Bible has shown that He is the moral law giver. First, although He put specific effort into Israel, God has historically judged other nations. Sometimes, this was merely by protecting Israel, or sending them to judge other nations, but even before Israel existed, God judged sinners. He was also somewhat active in the lives of gentiles. Interestingly, some ancient religions show enough similarities to Judaism to suggest that either God was moderately present with those cultures, or at the very least they maintained significant memories of God following the dispersion from Babel.
Second, through Jesus, God verified His identity. Even with our modern technology and scientific knowledge, we have not been able to replicate even half of Jesus' miracles. Indeed, the whole reason we have hospitals is because doctors can't just command people to be healed from miles away, like Jesus did. Death is especially irreversible. If you have someone who died 3 days ago, they aren't coming back, no matter how loudly you shout at their tomb. Jesus, however, was able to raise not only other people from the dead, but also Himself.
As for what God expects of us, the answer isn't simple. What He expects is literal perfection. We must live our entire lives doing only good, and no evil. It gets even stricter when you consider that passing on an opportunity to do good is also evil (James 4:17). I don't think I really need to explain that none of us have succeeded here, as our very conscience testifies of our imperfections even lacking God's specific laws. Having God's laws only makes us more aware of how wretched we really are.
So, what's the solution? There is a God, He has specific rules for us, we've broken those rules. Simple justice requires that our sins be dealt with. So, where do we go from here?
To the cross. Jesus' death was not an accident, neither was it a case of God being overpowered by men. Rather, Jesus lived a perfect life, yet He suffered a sinner's punishment. This, He did on our behalf. God can now legally dismiss our case, because rather than punishing us, God punished Jesus. We can therefore be rewarded for His goodness instead. But there is a catch. Salvation requires faith. We must believe that He died and rose again.