The same way we understand John 14:10:
Believest thou not that I am in the Father, and the Father in me? the
words that I speak unto you I speak not of myself: but the Father that
dwelleth in me, he doeth the works.
That something more transcendent than physical oneness is intended can be seen by flipping ahead a few chapters to the great intercessory prayer. In John 17:
6 I have manifested thy name unto the men which thou gavest me out of
the world: thine they were, and thou gavest them me; and they have
kept thy word.
11 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
22 And the glory which thou gavest me I have given them; that
they may be one, even as we are one:
23 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
26 And I have declared unto them thy name, and will declare it:
that the love wherewith thou hast loved me may be in them, and I in
Notice also the similar language in John 14:20
At that day ye shall know that I am in my Father, and ye in me, and I
Jesus speaks of His disciples being one with Him in the same way He is one with the Father. That the disciples are distinct beings from Jesus is not in doubt. In what sense then are they one? And in what sense will the Father and the Son make their abode with the disciples?
The Love of God
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 14:23)
In both chapters 14 & 17, the discussion of oneness is immediately accompanied by a discussion of love. When God’s love is in us—genuinely—we do God’s works. Jesus had the Father’s love in Him perfectly, and He did Father’s work perfectly (see John 14:10).
Love brings unity in a transcendent way—and Jesus wants that love to dwell in His disciples to make more of them—and their labors—things that could never be achieved on their own (see this applied in the parable of the vine in John 15:1-12). He does not wish for them to obey out of fear, transactional incentive, or even duty—He wants them to obey out of love.
He’s going…but not leaving?
But there’s more. In both chapters 14 & 17 the discussion of oneness is accompanied by a discussion of going to the Father. That the Father is not physically present is evident by Jesus’ repeated statement that He’s going somewhere else.
Much of the context of chapter 14 is seen in verses 2 & 3:
2 In my Father’s house are many mansions: if it were not so, I would
have told you. I go to prepare a place for you.
3 And if I go and prepare a place for you, I will come again, and
receive you unto myself; that where I am, there ye may be also.
Jesus has indicated that there is glory for His disciples—apparently some now and some hereafter. Jesus is telling them that He is preparing a place for them in heaven—but that they can experience Divine presence before then—the promise He gives in this chapter, right after the discussion of love, indicates how this can happen:
The Holy Ghost
26 But the Comforter, which is the Holy Ghost, whom the Father will
send in my name, he shall teach you all things, and bring all things
to your remembrance, whatsoever I have said unto you.
27 Peace I leave with you, my peace I give unto you: not as the world
giveth, give I unto you. Let not your heart be troubled, neither let
it be afraid. (John 14:26-27)
The discussion has now gone full circle from verse 1—Jesus told them not to be troubled and explained to them the Comforter He would give them. He’s leaving them in the world, but He is not leaving them without His or His Father’s companionship, through the Holy Ghost.
Jesus in John & Paul in Ephesians speak not of physical things, but of spiritual things. Despite having plainly told them He is going away (He’s about to die, and will before long ascend to heaven), He has promised that He will come to them, and He will soon pray that they may be one with Him. This coming will not be constant physical companionship, but the inestimable gift of the Holy Ghost:
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.
18 I will not leave you comfortless:
I will come to you. (John 14:17-18)
The Holy Ghost is a perfect representative of Jesus & the Father; Jesus is a perfect representative of the Father (see verse 9). The unity of the members of the Godhead is given in chapter 17 as an example—Jesus wants His disciples to become more perfect representatives of Him. One won’t lead you anywhere different from where another would. In the case of the Godhead, you cannot please one without pleasing all; you cannot truly worship one without worshipping all. Jesus promises the disciples that if they love Him and keep His words, they can enjoy the constant presence of a member of the Godhead.
In this way, Jesus has always had His Father with Him. In this way, Jesus will come to them, make His abode with them, dwell in their hearts, and be one with them, even while not physically present.
Note that all of the above was presented using only the Bible. If you'd like Book of Mormon references teaching these ideas, Alma 34:34-36 is a worthwhile place to start.