You can use polishes with hand but quite often they're more difficult to use by hand since you have to break the polish down. Basically, as you polish, the bits of polish break down further and further. A bit like going from rough sandpaper to supersmooth sandpaper. It's much easier with a machine.
There's a link on detailingworld in the Guides section. On iPhone so a bit awkward to link. It tells you how to use a polisher. Basically, prep the polishing pad with some quick detailing spray, place four skittle-sized blobs of polish on the pad. Then place the pad on the car and set the polisher at its lowest speed. Then move the machine around to spread the polish over a small area eg 12in by 12in. Then increase the speed in increments and continue to move the polisher, breaking down the polish into ever finer particles.