The Reformation brought to light the truths that have been called the five solas: sola scriptura (Scripture alone), sola fide (faith alone), sola gratia (grace alone), solus Christus (Christ alone), soli Deo gloria (God's glory alone).
Now we need to be clear, the Reformers didn't invent these truths, they simply rediscovered them, as they had long lain hidden under the clutter and mess of ecclesiastical tradition and confusion. These are truths that are openly and often taught in the Bible, and there's one passage I want to draw your attention to in which three of these solas are affirmed.
And that from childhood you have known the Holy Scriptures, which are able to make you wise for salvation through faith which is in Christ Jesus. All Scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness, that the man of God may be complete, thoroughly equipped for every good work.
In this passage Paul proclaims sola fide, solus Christus, and sola scriptura. Take a look.
Sola Fide
He says that salvation is through faith. Now when the Bible talks about faith, it doesn't use the word as so many use it today, i.e. to mean the opposite of reason or evidence. In the Bible faith is opposite to works.
There are many passages that teach that salvation is not obtained by any works of ours (e.g. here). Now this makes perfect sense when you think of it, because how much work would you have to do to earn the acceptance of an absolutely righteous, intrinsically holy, infinitely sin-hating God? Surely the answer is we would have work perfectly, doing all that His moral law demands and His holy will desires.
But none of us have done that, so rather than works commending us before God, works actually condemn us before God, because we haven't done what we ought to do, and we have done what we ought not do. We have fallen short of God's standard, and transgressed His law (Romans 3 v 19-23), and what that means is that even if we could be perfect from now until the day we die, it doesn't do anything to remove the sins of the past, it just means we aren't adding any further sins to the list - it does nothing to get us out of the danger we're in.
This is why acceptance with God cannot be by works, and must be by faith. We need to trust someone else to deliver us from danger. We need to rely on another to bring us into a right relationship with God. Therefore, Paul says here, as he says in so many other places, salvation is by faith.
Solus Christus
But Paul doesn't just say that salvation is by faith, he says that salvation is by faith in Christ Jesus. You see, it's not just a matter of having faith, your faith has to be placed in the right object. I used to work with a woman who told me she had very strong faith, and so she did, but her faith was placed in something that was empty and powerless.
Imagine you need a life-saving operation, and you come to me and tell me you want me to do the operation. I look at you with shock and tell you that I can't do it, I'm not fitted, qualified, able or experienced to do that, and you tell me that you have great faith in me. Can you see that the strength of your faith is irrelevant, because you've put your faith in the wrong person. However, you could commit your case to the care of the surgeon - the one with the qualifications, skill, ability and experience, and you could put your life in his hands with fear and trembling, but the weakness of your faith is also irrelevant because you've put your faith in the right person. Your safety doesn't depend on how great your faith is, it depends on the greatness of the one you put your faith in. So it is with the matter of salvation, what counts is not the strength of your faith, but the strength of the object of your faith. Only Jesus Christ has the ability, qualifications and fitness to save sinners, and He's got plenty of experience too! He alone can save because He is the only Person who has paid sin's penalty - He did this at the cross, and God declared that He did it by raising Him from the dead.
So salvation is by faith alone because we can't work for it, but salvation is by faith in Christ because He's done all the work for it.
Sola Scriptura
In this passage Paul tells us that the Scriptures are able to make us wise for salvation, so the bible is sufficient to tell us how to become Christians, but he goes on to tell us that the Bible is also sufficient to tell us how to become complete and mature Christians - he says it is through the Scriptures that the man of God may be complete, thoroughly furnished (i.e. like a ship being fully fitted out - having all it needs for the voyage) unto all good works. To put it another way, the Bible is not only sufficient for telling us how to become children of God, but it's sufficient for telling us how to become men of God.
In the voyage of the Christian life, it is the Bible that makes the believer fully fitted out. So what is implied in Paul's words is this, that there is nothing the Christian needs outside the pages of Holy Scripture to make him a complete, mature, thoroughly furnished Christian - it's all in the Bible. That's not to say we can't look outside the Bible for help to understand what's inside the Bible, but that really is the point - it's all about understanding what the Bible teaches, for that is what Paul says the Christian needs.
We can see then that these solas are not recent inventions, but fundamental foundations of Christianity which every saved soul will affirm.