God has graciously given us what we need in order to discern truth. The Bible is the revealed mind of God and is "given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness:" (2 Timothy 3:16) The Bible is where we begin, and end, the investigation of spiritual truth.
You are capable of discerning truth. You may think that you need some special calling within a church in order to discern the truth of God. While it is true that God must open spiritually blind eyes before they can see His truth (Acts 26:18), God has equipped you with a reasoning mind, a soul, a body, and made His revealed mind available to you in the Bible. Be as the Bereans to whom Paul preached. These were said to be "more noble than those in Thessalonica, in that they received the word with all readiness of mind, and searched the scriptures daily, whether those things were so." (Acts 17:11)
There is a host of scientific evidence for the reliability of the Bible and there are plenty of websites that go into this data. However, the objection to the reliability of the Bible that Joseph Smith gave was that it had lost many parts that were plain and precious (Second Nephi 29:3, 6, Teachings of the Prophet Joseph Smith, pp.10; 327). Since this is the objection raised, this is what will be specifically addressed here regarding the reliability of the Bible.
It is rather simple really, Jesus believed and quoted the Bible and therefore sanctioned its accuracy. If you think that Jesus, Himself, was mistaken, then He was not perfect and not able to be our Savior. Let's flesh this out a bit more. Jesus believed the Bible as it existed in His day. This would have been what we now consider the Old Testament. With the discovery of the Dead Sea Scrolls, we have a record of much of the Old Testament that predates Jesus' life on earth. Therefore, we know what the Old Testament records consisted of when Jesus believed it. When considering the content of the Dead Sea scrolls with our previous manuscript evidence, there is no significant disagreement. We can say with surety that the Old Testament has been preserved and is reliable, not only because of mountains of manuscript evidence, but more importantly, because Jesus Christ believed it, quoted from it, and told others to believe it.
Likewise, the New Testament is also trustworthy. With over five thousand Greek manuscripts, eight thousand Latin manuscripts, and numerous manuscripts in other languages, there is no room to doubt the reliability of the New Testament we have today. (For further information and study see The New Testament Documents: Are They Reliable? by F.F. Bruce)
A few additional objections need to be covered as well. The first is the objection that the Bible has been translated and transcribed so many times that it is most certainly different now than when it began. There is no solid evidence that this is the case. Additionally, it flies in the face of the mountains of manuscripts that indicate the opposite, that the content of the Bible has been meticulously preserved.
The second objection is similar to the first, it goes something like this: "The Bible was originally written in Hebrew , Aramaic and Greek. It had to be translated from Hebrew, there are no Aramaic manuscripts, only Greek translations, and no manuscripts exist that were written by the author's hand. Something is lost in the translation. Only a prophet can help us understand the original truth." This is somewhat of a catch-all argument. It rests upon the absence of a particular type of evidence, the "original authors," the manuscripts penned by the hands of the writers of the Bible. Bible scholars readily admit that we don't have these "original authors," however, there is so much evidence that the Bible we have is correct, it would be plain foolhardy to hold onto this argument. In fact, this is a form of a logical fallacy known as Argumentum Ad Ignoratiam or an Appeal to Ignorance.