Not much.

A black hole isn't a magic cosmic vacuum cleaner. It's a dense piece of mass. An asteroid mass black hole the size of a hydrogen atom would be... an object the size of a hydrogen atom with the mass of an asteroid. You could orbit it and the orbital calculations, at a reasonable distance, would be the same as orbiting an asteroid. You just can't get too close or you get into that steep gravity well and "become physics" (spaghettification etc.).

It would have an insanely steep gravity well, but you'd have to get close to actually feel it. It would rarely interact with mass naturally. We could chuck stuff into it or fire lasers and particle beams at it to study it, of course, but to hit it we'd have to fire it at the right angle and velocity to negate the orbit and fall into it. Orbital mechanics still works the same way.

If a black hole this size flew through the Earth at high velocity, it might not even do anything. It'd be like a bullet being fired through a puff of smoke. It might leave some kind of trail if you knew exactly what to look for and where to look, something almost analogous to the trails left by particles in a chamber.

I've given this example multiple times because it illustrates the point well, I think.

If you could magically transform the Moon into a black hole of the same mass, you would now have an object of that mass about the size of a BB or a small marble orbiting the Earth right where the Moon's center of mass orbited. The tides would continue as normal, since its gravitational effects on the Earth would be the same at that distance. Probes and other objects orbiting the Moon would continue to orbit it.

You just wouldn't be able to see it anymore. If you focused a very good telescope on its location, though, you could probably see gravitational lensing of the star field behind it.

The only risk might be if a large object actually hit it, in which case the accretion disc might temporarily emit enough X-rays and gamma rays to be harmful to Earth. Not sure though. It might not be that harmful at that distance.