Omnipresence baffles reason. How can someone be at all places at the same time? To say that the doctrine of divine infinitude implies omnipresence is not enough, for God is not an infinite ocean that fills all space, analogically speaking; He is a person. Therefore, the doctrine is a pure tenet of faith. Human attempts to explain omnipresence may either pluralize God as immanent to all things (pantheism) or reduce all things to a mere manifestation of the One (monism). Polytheism has no place for omnipresence. Indubitably then, the doctrine that the personal God is omnipresent is a pure tenet of faith that baffles all explanation. But, we can delineate a few implications from the doctrine:

1. Omnipresence doesn’t mean occupation of all space. Material objects occupy space. But, God is Spirit. Divine infinity doesn’t mean that God’s infinite presence takes up all space for anything else; which is, obviously, not the case. God’s presence in the world, therefore, cannot be detected by physical instruments of any kind; for, God is Spirit.
2. Omnipresence doesn’t mean divine distribution over all space. If I say that a table is present in my room, it means that different parts of the table occupy different parts of the space in the room. However, God, as Spirit, is not composed of parts; so, omnipresence is not to be imagined in corporeal terms. Of course, Scripture does talk figuratively of God as enthroned in heaven with earth as His footstool; however, these only express the fact that God rules over the universe and that the earth is at His feet. It also expresses the supremacy of God over all sizes whatsoever. This doesn’t mean that God can be divided into parts. St. Augustine (354-430) observed it well:
Although in speaking of him we say that God is everywhere present, we must resist carnal ideas and withdraw our mind from our bodily senses, and not imagine that God is distributed through all things by a sort of extension of size, as earth or water or air or light are distributed. (Letter 187)

Nevertheless, he is not distributed through space by size so that half of him should be in half the world and half in the other half of it. He is wholly present in all of it in such wise as to be wholly in heaven alone and wholly in the earth alone and wholly in heaven and earth together; not confined in any place, but wholly in himself everywhere. (Letter 187)
3. Omnipresence doesn’t mean indwelling of every entity. Divine omnipresence doesn’t mean that God is present in all things as indwelling each entity, be it stone, atom, or an organism. Omnipresence is not indwelling presence. God is everywhere doesn’t mean God dwells everywhere. The Scripture makes it clear that God dwells in heaven and that God indwells those who receive Him by faith.
4. Omnipresence means that God is fully present every-where. Our presence is material and finite; but, divine presence is spiritual and infinite. For instance, take God’s presence in relation to an area. God’s presence is full over 1000 in the same way that God’s presence is full over 1 or 1 sq.m. or 1 His presence over 1000 doesn’t mean that he is not fully present (or is only half-present) over 500 Now, we know that, conceptually, this divisibility of space is infinite. One cannot conceive of a point where one cannot divide space anymore. Nevertheless, one can talk of divine omnipresence as full infinitely everywhere.
5. Omnipresence means that God can do different things at different places simultaneously at the same time. This again, evidently, is a statement of faith.
6. Omnipresence doesn’t mean that God cannot move in space. The Bible talks of God’s presence moving with His people.
And He said, "My Presence will go with you, and I will give you rest."
Then he said to Him, "If Your Presence does not go with us, do not bring us up from here. (Exo 33:14-15 NKJ)
7. God’s presence everywhere doesn’t make the universe divine. The view that all things are divine because God is in everything is pantheism, which is antithetical to the biblical view of God as the Creator of all things. God’s presence is not affected by what happens to things.
8. It is fallacious to apply the physical concept of space-time to God’s omnipresence. Thus, I do not think it is right to talk of God’s omnipresence as applicable to time in the sense in which some talk of God as already being there in the future before we get there. This would also falsely mean that things are already there, in fact we are already there, before we get there (Then, in what sense does one talk of getting there?). Theology fails when it tries to comply with rational categories or empirical concepts; some of which are themselves controversial. The source of faith is hearing and the source of hearing is the Word of God, nothing else.
9. God’s omnipresence is not the same as His presence in heaven. It is also not the same as His indwelling presence in a child of God. Thus, while we can talk of God as present in heaven and also present in hell (Psalm 139:8), hell is certainly the opposite of heaven, and to be in heaven is to be with God while to be in hell is to be separated from the presence of God (2Cor.5:8; 2Thess.1:9).
10. Christ is present everywhere. But, Christ is ascended to heaven and is seated at the right hand of God (Heb.1:3). Christ is with His disciples (Matt.28:20). Christ indwells the believer’s heart (Eph.3:17). Christ is coming back for His church. And, when He comes back, we shall be with Him forever (1Thess.4:16-17). This might appear foolish to people and they may make fun of it. However, given the fact that God is Spirit and He is infinite, accepting the truth of divine omnipresence and also His special indwelling presence as well as His return is reasonable to faith.