1. God Himself is the standard of truth.
(John 14:6; Exodus 34:6; 2 Samuel 7:28; Psalm 25:10; Isaiah 65:16; Ephesians 4:21; Titus 1:2; 1 John 5:6)
2. Because of this, when God reveals things to us, we know that what He reveals is true. The Bible stands as an authoritative communication to us from God Himself, and we can often discern truth or falsehood simply by comparing a particular claim with Biblical revelation.
(2 Timothy 3:16; John 10:35; Acts 1:16; James 4:5; 2 Peter 1:20; Luke 16:17)
Christians know this because the Bible is our authority, and the Bible tells us this is so.
However, we can also see (1) via the impossibility of the contrary, or in other words, by demonstrating that not-(1) is clearly false, even beginning with non-Christian presuppositions, as long as we accept the veracity of the law of non-contradiction, which states that nothing can both be and not be at the same time and in the same way.
To do this, we begin by demonstrating that God definitely exists. If He did not exist, it would be impossible to know anything at all. We know that it is not impossible to know anything at all, therefore we know that God exists.
We next demonstrate that all the beliefs we come to accept, whether true or false, find their uncaused first cause in God Himself.
Here we must note the important distinction between what God causes and what God states or reveals. He may cause someone to believe something false. He may cause someone to lie. He may cause someone to speak incorrectly. But this is a dramatically different claim than the claim that God Himself lies or speaks incorrectly.
For example, if I take my dog out on a leash, and proceed very rapidly down the road such that my dog is forced to run, it could be said that I have caused my dog to run. However, if I am causing my dog to run by moving rapidly down the road in an automated wheelchair, I myself am not running. For me to cause my dog to run and for me to run are two dramatically different propositions. Likewise, for God to cause someone to lie, and for God Himself to lie, are two dramatically different propositions.
If direct and immediate (as opposed to indirect or mediated) communications from God were ever false, whether lies or simply errant, then there would be absolutely no way to confirm the truth or falsity of any belief whatsoever, since all beliefs find their uncaused first cause in Him. Since "the buck stops" with Him, if there were ever any doubt of His truthfulness or veracity, there could by definition be no higher authority by which to confirm it. We would never know whether or not anything were true or false, and we would have no way to confirm any belief. He is the appellate judge of truth, and without an honest judge, the truth can never be known.
In other words, if God were not perfectly truthful, knowledge would again be impossible. Knowledge is not impossible, therefore God is perfectly truthful.
Most importantly for each of us, the God who never lies has told us that we are all sinners, deserving of both death and damnation (Romans 3:23, 6:23; Matthew 8:12). He has further stated that if we trust in His Son, Jesus, who made things right for us through His own death (Hebrews 2:17; 1 John 4:10), we can be saved from destruction (Romans 10:9). If you have not yet put your trust in Jesus Christ for the forgiveness of your evil deeds, you have the promise of the one who is truth that if you do, you will be saved, and if you do not, you cannot be saved (John 3:18; Acts 4:12).
Repent therefore, and live (Ezekiel 18:32).