For the actual cables themselves (both derailleur cable and brake cable), you can use a diagonal cutter/plier. When cutting, try to apply pressure to cut through the cable fast - this will result in a cleaner cut and no fraying. If it frays a bit, don't worry as that's what crimping cable ends on are for.

Use the special cable cutter (Park Tool, et al) for shifter housing. If you by chance have a dremel tool already at your disposal, buy a reinforced cut-off wheel - this worked well for me. If using the dremel, try to cut through it fast as well as the heat may melt the plastic covering a bit.

You can use the diagonal cutter/plier for the brake housing.

For either of the housings, after you cut, make sure it's a good perpendicular cut. If not, file/sand it down. Then use a poke tool or awl to open up the hole all the way, as cutting may have squished the hole up.