When do I apply it, and how much should I use?
I mulch my perennial and shrub beds in spring, but not until after the soil has a chance to warm and dry a bit. I also am conscious of areas where I want biennials and other self-sown plants to have a chance to do their thing; mulching these too soon may prevent successful reseeding.
You want a 2- or 3-inch layer, generally speaking, and if you use the right stuff, about half of that will work into the underlying soil before you go to replenish in fall or the next spring.
Keep the mulch a couple of inches away from trunks of trees and shrubs; never pile it up, volcano-like, against them, as that can invite pests and diseases.
Anytime I work in an area and disturb the mulch, I add a bit more rather than leave bare spots. I apply mulch to new beds whenever I plant.
Mulch is sometimes also used in winter in cold zones to help keep newly planted things in the ground, or to shield tender plants from damage (such as the graft union on roses). For that purpose, materials like evergreen boughs (which would not normally be good for mulch) may also be used.