One of the best ways to prune the shrub lilacs and improve blooming is to thin out the interior of the shrub by pruning out (cut to the ground) 20% of the stems each year. Cut some of the oldest stems (up to 20%) and any weak, spindly stems right to the ground. This will keep your shrub nice and full with blooms from top to bottom. This type of pruning also allows good internal air circulation which will help prevent disease problems like powdery mildew.
If your lilac is very old and overgrown and hasn't been pruned for many years, often the blooms will be short, stubby, and at the top of the shrub where you can't see them. In this case, the best way to rejuvenate your lilac and get it blooming well again is to cut it hard - right back to the ground. The best time to do this is in March while they are still dormant but Mark Viette has had success doing this right after they finish blooming in late May. It will take 2 to 3 years for your lilac to bloom again but it is well worth the wait for the beautiful new blooms! The short lilac on the right was as overgrown as the one on the left when it was cut to the ground last June. After one year, it has beautiful lush new growth and will likely rebloom next spring with large, fragrant flowers!
Another less "dramatic" way to rejuvenate an overgrown lilac is to cut out 1/3 of the oldest stems each year for 3 years. New stems will grow up and replace these old stems and in three years, you will basically have a new shrub with the oldest stems being three years old. When rejuvenated in this way, you will always have some blooms on the shrub each year.