They cannot be seen by ordinary people, but everyone can feel the dark mood they press upon the area while they take in the good feelings and memories everyone had. Dementors reproduce through heavy mist. There is no way to kill a dementor, short of limiting their contact with any sources of its 'food' to the point that they starve. Aside from this, the only proven (and relatively easier) methods against dementors are the Patronus Charm (though it is difficult to learn), or staying in a sunny place, where they cannot be for long periods of time. However, these will only fend them off. They will follow whoever can provide them with the most 'food'.
They are capable (and more than willing) to suck a person's soul out of their body using the Dementor's Kiss, which unfortunately will not work on Mary Sues, given that they have no souls. Some Dark!Sues may have control over them, and Dark!Evil!Harry Stu is often fond of having Dementors nearby; either scenario is a very dangerous situation for the agents involved. Agents should under no circumstances attempt to fight one, or fight a Sue in the vicinity of one.
Chocolate is especially helpful after having had to spend too much time near dementors, IE, any amount of time whatsoever.