The best time varies, depending on which type of evergreen (conifer) that you want to trim (prune). Here's a quotation from "Pruning Trees and Shrubs," an Extension publication. You can follow this link to read the entire publication:
"Spruces, firs, and douglas firs don't grow continuously, but can be pruned any time because they have lateral (side) buds that will sprout if the terminal (tip) buds are removed. It's probably best to prune them in late winter, before growth begins. Some spring pruning, however, is not harmful.
"Pines only put on a single flush of tip growth each spring and then stop growing. Prune before these "candles" of new needles become mature. Pines do not have lateral buds, so removing terminal buds will take away new growing points for that branch. Eventually, this will leave dead stubs.
Pines seldom need pruning, but if you want to promote more dense growth, remove up to two-thirds of the length of newly expanded candles. Don't prune further back than the current year's growth.
Arborvitae, junipers, yews, and hemlocks grow continuously throughout the growing season. They can be pruned any time through the middle of summer. Even though these plants will tolerate heavy shearing, their natural form is usually most desirable, so prune only to correct growth defects."
Go to the Sustainable Urban Landscape Information Series (SULIS) site for photographs of conifers to identify which ones you have growing. Here is the link: