Your lilies have done what lilies do - once they've bloomed out they won't reflower this season. For now, just snip off the "candelabra" arms where the flowers were attached so it doesn't set seeds. Let the stem gradually yellow and brown out over the season and cut it back in the fall. I usually leave an inch or two of the stem sticking out of the ground so I know where they are and don't accidentally dig or plant over them. They don't need a lot of water; don't like their feet wet which could cause the bulbs to rot. Pixies multiply, so you might well get several more stems next season, each with a nice bud count.

The old salvia blooms can be pinched off, removing only the uppermost pair of leaves in the process. This will help the plant stay bushier and could well result in a rebloom. Any reblooming won't be as lush as the first. Am a little unsure of the water requirements for salvia, but they have a pretty good root system so perhaps a once a week deep watering is better than every other day. The ones I have are established and we've had fairly regular rain. I just cannot recall if salvia gets a little wilty looking when they need water.

Should I snip each individual arm or cut the stem itself (just below where the arms start to branch off)? Also, I've noticed that the some of the leaves (or foliage, whichever is the correct term) at the base of the plants are starting to "brown out".....is this where they would normally start wilting or should it be from-top-to-bottom?

I generally just snip off the arms since the seeds start forming at the very ends, but it wouldn't hurt to snip off the whole candelabra just below where it is attached to the stem. The stem doesn't yellow/brown out in any particular pattern - sometimes pretty close to all at once, sometimes a leaf at a time. The bulb is feeding itself on the stem, storing energy for next season, so the longer you leave it the better for the bulb. The stems will vecome very dry and brittle when all of the energy has gone back to the bulb. Can look a little messy, so I'll often plant in front of them to hide the old lily foliage.