Hard drives are purely magnetic - tiny spots on the disks are magnetized one way or another, to record the data. These are arranged in concentric rings called tracks (or cylinders). When the heads are aligned with a particular track, the spinning of the disk, causes the magnetic bits to fly under the head, causing the head to pick a signal which can be processed by the drive electronics. To write, a strong electrical current is passed through the head, which causes the spot on the disk directly under the head to be remagnetized.
Very primitive hard drives used motors, with fixed movements. E.g. the head motor could move in steps of 0.01", and the heads had to be carefully aligned to the disks at the factory. There was some experimentation with removable floppy/hard drives using laser guidance, but on modern hard drives, self-guiding technologies have been developed:
The hard drive heads are able to find the track they want by counting the tracks as the head passes over them, and using sophisticated algorithms to track and adjust the trajectory of the heads so that they land precisely on the desired track. The design of the head is such that if it's not precisely aligned with a track, it doesn't pick up a signal, so by measuring the strength of the signal from the head, the drive controller knows when it's in the exact right spot.
There are potential future hard drive technlogies that might use lasers. One of the problems with hard drives is that the data bits are so small that when you record one, the magnetic field from the recording head leaks into neighboring bits and weakens them. Because it's much easier to magnetize hot material, some companies are experimenting with using precisely focused lasers to warm up the disk directly under the head, so that it can be magnetized more easily, causing less weakening of the cold neighbors.
Although not used in hard drives, it is possible to read magnetic disks with a laser. This is how magneto-optical discs work (these are rare, professional discs, but the same technology is used in re-writeable minidiscs). Magnetic fields cause reflected laser light to twist - this twisting can be detected by a suitable detector. When a MO disc is recorded, a laser is used to warm up the individual bit on the disc, then a magnetic field is applied, and as the bit cools off, it the magnetic field is locked into the bit. A weaker laser is used to read the disc using the twisting method. Unlike CD-RW/DVD-RW where the recording laser actually has to melt the recording layer, MO lasers only have to warm it up enough to make it more magnetizable. This makes the discs much more reliable and they can tolerate many more erase/record cycles.