I recomend using large fans for propulsion. Ever seen that Braniac episode where they make a hoverboard?

Lol yeah. Have you seen the one where they put blocks of cesium in a bath?

"Levitation" via magnetic repulsion is inherently unstable (the forces are such that a small deviation from perfect alignment is driven farther and farther away). Maglev trains counteract this instability with mechanical barriers, and by setting up pairwise repulsions along multiple axes which are mutually constrained. You can't use magnets to levitate against a ferromagnetic surface -- the external magnetic field necessarily induces a magnetization which is attractive (that's why magnets stick to iron plates :-). You can work this out yourself with a simple toy model. Treat the metal as a collection of randomly oriented little bar magnets. Bring a large magnet near it, and ask how the constituents will align themselves.

However an extremely powerful magnet could make you hover, or hover on water, think lifting frogs with supermagnets, I'm almost sure they use the diamagnetic properties of water...

The frog levitation is done inside a solenoid magnet (i.e., immersed within a dipole field. Hovering means you're using the exterior loops of a dipole (or more complicated multipole) field, which will be unstable.

Also the question asked was about hovering above a metal surface. With a sufficiently strong field, you might be able to produce a bearing ("hover") against a diamagnetic surface, but with fields that strong, I wonder whether there would be subtle neurological effects (which frogs can't exactly tell us about :-).

Now, if you kitted out your house with a floor tiled entirely in lanthanum cuprate ceramic (high-T_c superconductor) and replaced the radiant heat system with circulating liquid nitrogen....Hmmmm....

Though unstable a large field coming from a flat plate might be similar to standing on floats in a swimming pool, a human could potentially move along doing that by having a leg in front of them and another pointed out behind - obviously this doesn't work in swimming pools because there's no energy transfer... If you made yourself some powerful electromagnets and a rail system you could get a super low friction thing on the go like a maglev, however the energy involved would be huge I'd say, especially for something home engineered. By the way watch your inbox, got a little project you may be interested in.

....I've been thinking about this some more...I don't think you could do the levitation at all with a static magnetic field (either permanent magnets or simple DC powered electromagnets). The instability is going to get you.

However, you should be able to do something with an active feedback loop and electromagnets. I've got a toy on my desk, which uses electromagnets to suspend a ball with a permanent magnet in midair.

As the ball falls (even a little), the changing B field induces a current, which is sensed to increase the actuator current. As the ball gets too close, the same effect is used to decrease the actuator current.

I suspect you could do something similar, but more complex, to detect a deviation from balance and alter the levitation field to compensate. Whether such a system (with power supply, feedback circuit, and electromagets) could be built into a pair of shoes (snowshoes :-) is a separate question.

DIAmagnetic levitation - using bismuth or pyrolytic graphite IS statically stable, and doesn't violate Earnshaw's theorem.

Good point, Steve! It doesn't generally support much weight (yes, weight, for the non-physicist nit-pickers out there :-), however.

I don;t know if there are theoretical materials with higher diamagnetic effects ?

I thought of superconductors just after I posted, as I was imaging the flux patterns in the material !

I'd say the majority would have to go elsewhere, I suppose the tech's mostly there, I'd say looking over how a shuttle keeps adjustment for a certain angle would be interesting, the difference being the object itself is pushed, not pushing away...