For the sole and sufficient authority in Christianity, the Bible doesn't use the word "Christian" very often. It does, however, tell us everything we need to know about how to define it.
The key to understanding any word is understanding its first use. What a word is intended to mean the first time it is used is what it ought to mean today. This isn't always the case, of course, as words fall out of popularity, change meaning over time, and it's not even always possible to figure out when the word was first used.
The former problem may apply here, but the latter certainly does not. The Bible records the exact moment the word "Christian" was formed. Specifically, it was in Antioch, not too long after Paul's conversion. It was used to describe the disciples, and so we know that the word "Christian" has something to do with them. Specifically, it refers to the faith they all held in common. This is what gave rise to the word CHRIST-ian, because the faith they professed centred around this one figure, the Christ.
The second time the Bible uses the word "Christian" is in quoting Agrippa whom, having listened to Paul, said "you almost persuade me to become a Christian". Paul's response to Agrippa is "I would to God that not only you, but also all who hear me today, might become both almost and altogether such as I am, except for these chains." We see, then, that Christian is not a term designed to refer exclusively to the Apostles, but also to those who are "almost and altogether" such as the Apostles were (though preferably without chains attached).
The final time the Bible mentions the word "Christian" is in describing how we ought to conduct ourselves as Christians, especially with regard to persecution. 1 Peter 4:12-19 tells us to expect persecution as Christians, and not to be surprised when it happens. It tells us that we need to make sure we don't deserve the suffering that comes to us, but that we ought to "commit our souls to Him in doing good, as to a faithful Creator" (v19).
Combining all of this, we have everything we need to determine what the word "Christian" means. A Christian is "Someone who adheres to the faith the Apostles preached, according to the will of God".
Earlier in this article, however, I mentioned one difficulty that might be encountered when using the principle of first use to define Christianity. That is, when a word is commonly used in an alternate way to the way of its first use. This has happened with a variety of words throughout history. "Bully", for example, did not always refer to someone who is consistently cruel to someone without cause, but once meant "friend", as well as being used to express joy. You'll also notice that certain slang words seem to mean the opposite of what they should. If a teenager describes something as "sick", for example, he doesn't necessarily mean disgusting or an ill feeling, but for some odd reason, the term has come to mean "awesome" or "cool". So, the question is, has Christianity retained its archaic meaning?
The answer is yes in a way, and no in another. Just as words like "sick" retain their original meanings while simultaneously acquiring alternate meanings, so also has the word "Christian" developed a double, triple, maybe even quadruple meaning.
It does not need to be said that there are too many mutually exclusive religions, too many unBiblical/extra-Biblical traditions, and too many people who call themselves Christian in different ways for it to have the same meaning every time. A Mormon, for example, might claim to be Christian, but is evidently not a Christian in the same sense as I am. By the definition set in this article, it is fair to say that a Mormon simply is not Christian*, because the faith they profess is fundamentally different from the faith of the Apostles.
There are also those who do horrible things, whether separately from their professed Christian faith (we all sin), or in the name of it. It is a lot harder to discount Christians by their works, but it is nevertheless still possible. While Christians all sin, sometimes even egregiously, the Bible does say that we will recognise each other by our fruits. 1 Peter 4:19 also tells us specifically that Christians "commit their souls to Him in doing good, as to a faithful Creator", which is why I added "according to the will of God" on today's definition. Essentially, the heart is where Christianity is, and thus if you're "a murderer, a thief, an evildoer, or as a busybody in other people’s matters" (v15), the chances are you're not Christian.
But according to our culture (especially if your source is Google, Wikipedia, or a number of non-Christian sources), merely identifying one's self as Christian is enough to make one a Christian. Therefore, the word "Christian" and its variants are actually what's called a homonym. A homonym is a word which is spelled or pronounced similarly to another word with an alternate meaning. Park and park, for example, are identical in both spelling and pronunciation, yet one refers to a location of leisure, the other is the act of placing a vehicle in a specific location. Drink and drink are identical in both spelling and pronunciation, yet one refers to a physical object, the other refers to the action of consuming that object. Bird and bird are identical in pronunciation and in spelling, yet one refers to an animal, the other is a British slang term used to refer to a woman.
So, Christianity does have multiple meanings. A person, theme, or belief can be "Christian" in name without being Christian in nature. But for today, we don't need to address that much more. We have defined what a Christian is, in the Biblical sense.
*Note: The official position of both Path Treader Ministries and God Squad Apologetics is that there are true Christians in every denomination, but that the denominations themselves are not Christian. For further clarification, one cannot hold consistently to both the Bible and to unBiblical religions, and thus while one may self-identify as a Christian and a Mormon, one cannot CONSISTENTLY be both.