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Related to this question Where do magnets get the energy to repel?

If I have a magnet repelling another, eg one in my hand, the other being pushed along the desk, how do the each of the magnet's fields actually "push" against each other? What translates the magnetic field to kinetic energy?

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You are confusing force with energy. Energy is force x distance.

You are adding energy to a system when you slide one magnet (the one in your hand) along the table, forcing it closer to the other magnet. By doing this you are forcing the system (the two magnets) into a higher energy state. Every system (at least everyone I can think of) seeks a lower energy state. At some point in your slide, the forces build up until the magnet not in your hand breaks free of static friction and slides to a lower energy state (away from the magnet in your hand. The energy expended to move that magnet is the energy YOU stored in the system by forcing the one magnet near to the other.

Another way to think of it is in terms of potential energy. The erarth's gravitational field is not energy, BUT you can store potenial energy in a system by raising a weight to ahigher elevation within that force (gravitational) field. The energy is then reclaimed from the system when the weight drops. With magnets the story is the same, except that the potential energy is due to position in a magnetic field rather than in a gravitational one.

I could go into detail about how dipoles in a ferromagnetic material add up to create a magnetic field, or how you can create a magnetic field with no magnetic magnet at all; but I don't think that is what you are asking. Let me know if i missed the mark.

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    $\begingroup$ Strange that you've neglected any mention of how the force is transmitted by the B-field. I'm pretty sure this was what the OP asked, unless I've missed the mark ;) $\endgroup$
    – qftme
    Commented May 16, 2011 at 18:15
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    $\begingroup$ @qftme, haha, you're having fun that someone could be tortured by an unanswerable question, right? Feynman was asked the same question, why magnets work, and after some confused babbling - and successful efforts to regulate his anger about the stupidity of the author of the question - he said the right thing, that it's the wrong question because the magnetic forces are fundamental while what the asker can imagine and knows is not fundamental: youtube.com/watch?v=wMFPe-DwULM $\endgroup$
    – Luboš Motl
    Commented May 16, 2011 at 19:15
  • $\begingroup$ @Lubosh, lol, unfortunately not. Funnily enough, I came across that Feynman quote again yesterday, whilst re-watching Sidney Coleman's QMIYF. Actually I think an answer here is possible given that the OP didn't say "without reference to Maxwell's equations or vector calculus". My point was, I'm confident that it should be possible to illustrate how the force on the table-bound magnet is manifest from the change in flux density of the B-field, caused by the approach of the other magnet. Unfortunately my EM lecturer was pants so, personally, I don't feel confident enough to post a concise answer $\endgroup$
    – qftme
    Commented May 16, 2011 at 20:05
  • $\begingroup$ Hey if the question made Feynman angry I'm happy enough that its a good one. $\endgroup$
    – Justicle
    Commented May 17, 2011 at 4:29
  • $\begingroup$ @Lubosh if you post that video as an answer, its pretty much what I was after. $\endgroup$
    – Justicle
    Commented May 17, 2011 at 4:37

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