I don't believe in the deity being omnipotent, omniscient and omnipresent, but apparently most Abrahamic believers (not just Muslims) do. I, however, do understand this concept, and yet I don't see how it is possible, because the scriptures that I have read (not just the Qur'an), showed contradictions to any of 3 omni-s.
To further explain to you, pastek, about the Holy Spirit, which will hopefully help you understand the Christian belief about the Holy Spirit.
The omnipresent as you probably know what it mean, is that a deity is present everywhere, at the same time.
Supposedly god can listen to (if not answer) everyone's prayers at the same time. The manifestation of spirit of God that listen to these prayers, and possibly reveal its guidance as "answers", supposedly come from the Holy Spirit.
Not all aspects of god are manifested to people.
To give you understanding what I mean by this aspect or manifestation, I will give you an example.
God is like an actor. Whether it be in a movie set or on stage, an actor may have several (or more) different roles that he must play for either the audience (if on stage) or in front of the camera (in film or on TV). The actor is supposed to only show one character for each role he would play, and not the characters of other stories, and not his private life.
So to tie it all together, the god that is not seen is like the private moments of the actor's life. The Holy Spirit is like manifestation of actor's one of the characters for that particular story (a film role, or a play).
No one is supposed to see the real god, until a person get to live near his presence in the afterlife in heaven, but the Holy Spirit is the nearest thing (the one aspect of god) that a person be close to, while alive and on earth.