How are atoms manipulated?
In general, one usually doesn't work directly with single atoms, though there are ways to do that as well, usually involving scanning probe microscopy (basically poking at atoms with very sharp probes to either manipulate them or just image them).

Atoms become much easier to work with when they are are ionized and can be manipulated by electric or magnetic fields (atoms have neutral charge so the Lorentz force can't be used to control them). Even then, most techniques deal with small groups of ions rather than individual ones. Ions are relatively easy to manipulate and we can easily trap them, accelerate them into beams, and focus them. The LHC is, of course, a very impressive (and expensive) example of this. The way it works is that packets of ions are accelerated by electric and magnetic fields to form two ion beams, which are then focused into a very small area and made to intersect, allowing the ions to collide and all the cool particle physics stuff to happen.

Manipulation of ions is also used in countless other scientific applications: semiconductor manufacturing, surface analysis, medical analysis, radioisotope dating, to name a few.