How slasher scenes get shot?

Having been in the makeup FX biz for a while, I am in a good position to answer this, but I'm going to do so using personal experience and no links to external sites - so you might want to wait for a more comprehensive answer before up voting.

Essentially, there are several ways to approach these shots.

Let's take a simple stabbing: If the stabbing is carried out through clothing then all that is required is a blood bag (or blood pumping knife), a retractable blade and your actors. The retractable blade goes in, the knife handle is squeezed to achieve the blood or the blood bag is burst to create the same effect. Bare skin is a little harder, but will still utilize the same retractable blade - however more often than not a cut away will edited in (reaction shot etc) so that the preceding shot can feature a prosthetic (latex, silicon, foam rubber) that simulates the wound. This prosthetic might even feature a blood tube (hidden by clothing or hairline) that can make blood seep from the gash.

More complex effects (bodies ripping in half etc) will require full size fabricated torsos, made to look like the victim and loaded with fake (or real) organs and blood. Infamously, for the torso ripping scene at the climax of the original Day of the Dead, Romero loaded the actor's fake stomach cavity with real guts, which got very ripe under the lights. The zombies had their nostrils plugged, but poor Joe Pilato who played Rhodes had to suffer!

These old school gore effects are still utilized today, most noticeably by KNB FX who create the effects for The Walking Dead, but even those effects are combined with CGI to show blades passing through heads. In fact, CGI has become the standard for lower budget productions (see anything on the SyFy channel) for creating these types of effects, but they are usually shoddy, fake and unbelievable (I'm an old school guy, so I may be a little prejudiced here).

If you require more detailed information about the entire practical effect process, I would be happy to add that to my answer. Bear in mind though it will turn into an essay :)