So I think first we must define what a principle is and what an ordinance is. So first off, a principle is "an underlying faculty or endowment" and an ordinance is "a prescribed usage, practice, or ceremony." So what that is saying is that a principle is a basic need that's established, like faith, and an ordinance is something that is performed, like baptism. (Definitions came from Merriam-Webster Dictionary)
Now that we have that established we can get into what the first principles and ordinances are. The first one being, "Faith in the Lord Jesus Christ." So what is faith, and why do we need it? Faith as explained in the scriptures is, "faith is not to have a perfect knowledge of things; therefore if ye have faith ye hope for things which are not seen, which are true." (Alma 32:21) So we must hope for things that we can't see, but we know are there. It's like the air we breathe, we can't see the air but we know it's there. It fills our lungs every time we take a breath, and so it is with Jesus Christ and our Heavenly Father. We can't see them, but we can still know that they are there. We can feel the Spirit, and we can have their influence in our lives. We need faith in our lives so that we can know who to turn to in our times of need. It is what gets us through those hard times and picks us up when we are down.
Second is repentance. What is repentance? Repentance is a change of heart. It is turning away from the thing we don't want in our lives and adding something we do want in our lives. There is 5 steps to repentance: 1) To acknowledge that we are sinning, 2) be sorry and feel godly sorrow, 3) confess to God, 4) correct the mistake, and 5) endure to the end. As we apply these five steps in our lives, our lives become so much easier to handle and to get through. It's not making big changes, but the small ones that really add up to making big ones.

Fourth, the Gift of the Holy Ghost by the laying on of hands. This is also known as the baptism by fire.The gift of the Holy Ghost is so very important. It is the purifying, or sanctifying, part of baptism. The gift of the Holy Ghost allows us to have the constant companionship of the Holy Ghost. This can help us stay closer to our Heavenly Father, and to have to ability to be guided in all things. The Holy Ghost provides comfort, protection, and revelation.
These are the first principles and ordinances of the gospel. We know that we need to continue on and endure to the end in order to live with God in the end. These are just the beginning. I love this gospel. It is so simple and allows all to come closer to Jesus Christ.