I understand at one time Satan was an angel in Heaven, the most beautiful. I have often wondered where his sin derived from to want to "take over". As I understand it, he was the one to start "tempting" to cause Eve to sin, but what caused his sin to become what it led to?

The question has been asked as to how Satan could sin if he were created perfect. First of all, we need to understand that this is a fact stated in scripture. Ezekiel 28:15Thou wast perfect in thy ways from the day that thou wast created, till iniquity was found in thee.
See All... says of Satan, "Thou wast perfect in thy ways from the day that thou wast created, till iniquity was found in thee." So we know that he went from perfection to having iniquity. However, this is not satisfying to many people. They reason thus:

1. God is absolutely perfect.
2. God cannot create anything imperfect.
3. But perfect creatures cannot do evil.
4. Therefore, neither God nor His perfect creatures can produce evil.

To many, this seems to be the perfect argument to discredit the scriptures and Christian doctrine, but it is not. Here is a true solution to the problem:

1. God is absolutely perfect.
2. God created absolutely perfect creatures.
3. One of the perfections God gave some of His creatures was the power of free choice.
4. Some of God’s creatures freely chose to do evil.

Therefore, a perfect creature caused evil.

Higher created beings had to have greater abilities than lower ones. One of those abilities is the power of free choice. God wanted creatures who served and worshipped Him because they chose to do so. That is not possible without free choice. However, the ability to choose rightly is also the ability to choose wrongly. Satan fell of his own choice being lifted up with pride. Consider his willfulness in the following passage:

Isaiah 14:12-14 [12] How art thou fallen from heaven, O Lucifer, son of the morning! how art thou cut down to the ground, which didst weaken the nations! [13] For thou hast said in thine heart, I will ascend into heaven, I will exalt my throne above the stars of God: I will sit also upon the mount of the congregation, in the sides of the north: [14] I will ascend above the heights of the clouds; I will be like the most High.
See All... How art thou fallen from heaven, O Lucifer, son of the morning! how art thou cut down to the ground, which didst weaken the nations! For thou hast said in thine heart, I will ascend into heaven, I will exalt my throne above the stars of God: I will sit also upon the mount of the congregation, in the sides of the north: I will ascend above the heights of the clouds; I will be like the most High.

As stated in 1Timothy 3:6Not a novice, lest being lifted up with pride he fall into the condemnation of the devil.
See All..., Satan fell from being lifted up with pride. He decided that he did not want second place to God. He wanted to rule-- not serve. His own free will brought sin into the world.