Do me a favor, would you? Will you carefully consider this answer, which comes directly from the KJV of the Bible. In most cases, I have even included the text, rather than simply refer to the passages.
The Bible teaches that God is one. Among other passages, in John 10:30 learn that the Father and the Son are one. Yet in many other passages, there is a clear distinction in the beings themselves. For example:
John 14:28 Jesus proclaims that the Father is greater than Jesus is.
John 17 The great intercessory prayer. Jesus prays to the Father, not as an example of prayer, but for real needs.
John 16:7 The Comfortor would come when Jesus went away. "If I depart, I will send Him unto you."
Matthew 3:16,17 Jesus is in the water, the Holy Ghost comes down and lights upon him like a dove, and the voice of the Father comes from heaven, testifying that Jesus is His Son. (See also John 12:28,29)
Gen. 1:26,27 "Let us make man in our image" demonstrates a plurality.
Matt. 12:31,32 Sins against the Holy Ghost and against the Son are distinguishable.
John 8:17,18 Jesus refers to the law, wherein it states that the testimony of two men is true. He then states that He is one that bears testimony and the Father is another. Note: If they were not two beings, they would not have satisfied the Jewish law, requiring the testimony of two men. Thus, the point that Jesus was making would have been pointless.
Revelation 1:6 Jesus has made us kings and priests unto God and His Father.
John 20:17 Jesus ascends to the Father.
Acts 7:55,56 Stephen, being martyred, sees the Son on the right hand of God. Hard to miss this one, unless you refuse to take the Bible literally here.
For the sake of "white space", I won't include some of the other verses in the Bible that clearly demonstrate a plurality and a seperateness with the Father, the Son, and the Holy Ghost.
How do LDS believe that there is one God, yet clearly seperate and distinguishable beings? This is a clear and simple doctrine, for the Lord Himself gave the answer. It is found in John 14 and 17, in several passages, in context, and it is clear. They are "one" in the very sense that we are to be one with them. This is not so difficult to understand. Consider these verses:
John 14:23
Jesus answered and said unto him, If a man love me, he will keep my words: and my Father will love him, and we will come unto him, and make our abode with him.
John 14:17
[Even] the Spirit of truth; whom the world cannot receive, because it seeth him not, neither knoweth him: but ye know him; for he dwelleth with you, and shall be in you.
John 14:20
At that day ye shall know that I [am] in my Father, and ye in me, and I in you.
John 17:10-11
And all mine are thine, and thine are mine; and I am glorified in them.
And now I am no more in the world, but these are in the world, and I come to thee. Holy Father, keep through thine own name those whom thou hast given me, that they may be one, as we [are].
John 17:20-23
Neither pray I for these alone, but for them also which shall believe on me through their word;
That they all may be one; as thou, Father, [art] in me, and I in thee, that they also may be one in us: that the world may believe that thou hast sent me.
And the glory which thou gavest me I have given them; that they may be one, even as we are one:
I in them, and thou in me, that they may be made perfect in one; and that the world may know that thou hast sent me, and hast loved them, as thou hast loved me.
Clearly the Lord was not praying that we all become of one essence. We are to be united as are the Father, the Son and the Holy Ghost, in love and purpose and perfection.Yet Jesus Himself claims that as we become one, we will be one in the same manner that He and His Father are one.
Now, I have answered your question. I am rather certain that you will not now run out and ask for baptism in the LDS faith. But I have demonstrated that the LDS position on the Godhead is Biblical. Will you now answer the question that I have asked? Where is the external evidence of the resurrection of the Savior, Jesus Christ? I am still very willing to answer this question, for it does have one.
Be blessed!
Don