What Makes a False Religion, False?

Left, a Muslim woman in a hijab. Right, Catholic nun in her habit.

If it's not one false religion, it's another. False religion has been with us since the Garden. It's nothing new. When Jesus returns, He mused whether He will even find faith upon the earth. (Luke 18:8)
The question of the day is, what makes a religion false?
Humans have an innate sense of worship. We don't worship who God wants us to worship. We don't worship in the way He wants us to worship. We don't worship for the right reasons.
Examples of these are of course, Adam and Eve, who were tempted into worshiping themselves ("you will be like God".) Cain did not worship in the right way. (Genesis 4:3-5). But there is a right way to worship and a wrong way to worship. Neither did Nadab and Abihu. (Leviticus 10:1). Many in the days of the Incarnation did not worship Jesus for the right reasons. They preferred the glory of men to the glory of God. (John 12:43).
I've spoken with non-saved people who think that God was being too harsh for preferring Abel's blood offering and by rejecting Cain's offering of the fruit of the ground. As if God is someone who should be happy with whatever worship we throw at Him. As in our own earthly lives, there are standards. Even unsaved people know that. Parents have standards for children's behavior, bosses have standards for evaluating their employees, factories have standards of production to ensure a quality product. When it comes to God though, people think that no standards is the more "loving" way.
Not so. There was a spy spoof TV program in the 1960s called Get Smart. Max the bumbling, incompetent spy used to say "Missed it by that much."

Obviously, this phrase was used when someone, usually Max,
was just a little bit off in his aim, guess, or goal.
Missed it by that much!

And because the path is narrow, it is easy to miss the mark.
However when it comes to faith and worship, missing it even by that much means the wrong eternity. Jesus said the path is narrow. (Matthew 7:13). Though we can never fall off the path once we are on, those who are not saved concoct all manner of methods to save themselves.
For example, in Japan, we learn that it was thought if you crawled through a volcanic "womb cave" you would be reborn.

For centuries, religious devotees, or ascetics, looked towards Mount Fuji as a place of worship, trekking up the mountainside to reap its spiritual powers. The mysterious lava caves were thought of as “human wombs,” and those who journeyed through the dark passageways could experience rebirth. ... The cave known as Tainai, which translates to "womb," is said to be the birthplace of Sengen, the deity of Mount Fuji.  It was common for the religious followers of the Mount Fuji cult to associate terrestrial features of the mountain with parts of the human anatomy. 

I won't go further into detail, though the articles does. Suffice to say that anyone passing through the womb caves of Mt Fuji and performing the rites there did not save themselves, nor did they cause their own rebirth.
In Catholicism, there are made-up salvation methods such as the Treasury of Merit and Indulgences. From his online class "Justification By Faith Alone," RC Sproul explains,

The treasury of merit exists so that people can get into heaven. Very few people die and go directly to heaven, according to the Roman Catholic view. The majority of people who die go to purgatory to have their impurities purged. Purgatory is not hell; it is not a place of punishment. People in purgatory do not have sufficient merit to get them directly into heaven. The few who go directly to heaven have sufficient merit as well as supererogatory merit. Works that go beyond the call of duty produce supererogatory merit. Supererogatory merit is more than is required to get into heaven, allowing for the excess to be deposited into the Treasury of Merit. When indulgences are purchased, withdrawals are made from the treasury of merit for those in purgatory.

Purgatory and Indulgences are weird. All that is just as weird as the volcanic womb tunnels.
There are many other weird methods to save one's self in many other false religions that we could go into but they are all complicated, weird, wrong, and bad.
The truth is so much simpler.
For by grace you have been saved through faith. And this is not your own doing; it is the gift of God, not a result of works, so that no one may boast. (Ephesians 2:8-9).
So what makes a religion untrue, or what makes Christianity true? There are some doctrines that the Bible declares as essential for true faith.

The Bible itself reveals those doctrines that are essential to the Christian faith.  They are 

1) the Deity of Christ, 2) Salvation by Grace, 3) Resurrection of Christ, 4) the gospel, and 5) monotheism. These are the doctrines the Bible says are necessary.  Though there are many other important doctrines, these five are the ones that are declared by Scripture to be essential. A non-regenerate person (i.e., Mormon or Jehovah's Witness, atheist, Muslim), will deny one or more of these essential doctrines. Please note that there are other derivative doctrines of scripture that become necessary also and the Trinity being one.

Also note that bedsides denying essential doctrines, a non-regenerate person may use the same terms as a Christian, saying things like "I have faith." Or, "I believe." They have adopted Christian terms but have through use or intent, redefined them to something they are not. Mormons for example, believe that Jesus is a god, so a superficial look at the essential doctrine that the deity of Christ is essential in that case would seem to satisfy. However, they believe Jesus is a created god, not THE Eternal, self-existent Father. So they deny the Deity of Christ even though they call Him a god. Therefore Mormonism is a false religion.
Catholics even use the term 'justification by faith' as born again believers in the true faith do, which is essentially what the Ephesians verse states. However, Catholics disbelieve the source of the necessary righteousness that justifies us is solely from God, but stems from an inner righteousness humans already possess or generate thought works.

Imputation has always been the one thing that has caused the many attempts to resolve the theological conflict of the Reformation to fail. Rome has always rejected the idea that we are justified on the basis of an imputed righteousness. The Roman view would be that the meritorious cause for God to declare a person righteous is because that person is righteous. The Reformed view would be that the meritorious cause for God to declare a person righteous is because Christ is righteous. (RC Sproul, online course "Justified by faith alone". 

The essential doctrines are expounded upon at the link above. Here it is again. Those are the doctrines the Word of God declare are necessary for faith. If there is any religion which alter those or are absent any of them, it is a false religion.
How can a Christian determine which doctrines are essential and which are not? Here are two bullet points from a short essay by John MacArthur

I. All Fundamental Articles of Faith Must Be Drawn from the Scriptures
II. The Fundamentals Are Clear in Scripture

Any religion which deviates from the essential doctrines, alters them, or puts forth doctrines that are not from scripture or are unclear, is not a true faith. ALL religions which rely on anything other than the word of God and which draws its essentials from the word are false.
Another way to determine if a religion is false is to see how it handles the Bible. False religions may or may not use the Bible as their basis. Jehovah's Witnesses use the Bible but they've re-written it. Mormons use the Bible but have added to it with their Doctrine and Covenants and Pearl of Great Price philosophies. Islam and Hinduism don't use the Bible at all.
Christianity is revealed to us through the Bible. It's one book, divided into 66 books, written over 1,500 years but is a unified, cohesive tome with a sole author. I'd encourage you to check out the link at CARM above which outlines the essential doctrines with the verses and explanations.
You might not have thought about it this way, but ALL OTHER religions have a sole author, too. Satan. He wrote the precepts of Mormonism, Catholicism, Hinduism, Jainism, Atheism, Buddhism, Islam, Wicca, and the rest. If a religion is not of God, it is of the devil. (Matthew 12:30). There are two paths, the broad and the narrow. There is either one or the other. (1 Corinthians 10:21, Matthew 6:24). Any religion that isn't Christianity is opposed to Jesus and therefore it is of the devil. Even religions like Catholicism, which miss it by that much.