When and how do you prune lilac bushes?

Best time to prune lilacs is right after they're through blooming. This gives the lilac bushes plenty of time for the new shoots to develop before the next season.

https://www.thespruce.com/pruning-lilacs-how-and-when-to-prune-lilacs-1403004

After flowering cut back each stem which has carried a flower to a nice pair of leaves. If you cut straight you may get some 'die back', however if you make a slanting cut just above the leaves they should grow away quite quickly. Another easy way, is to cut some stems in bud and put them in a vase in your home. Pruning is then already done, easy.

If you like to cut bouquets you should cut them back enough that you can reach them after the regrowth.