Lilacs form flower buds for the next year after blooming during the current year. Lilacs should be deadheaded immediately after blooming to encourage good bud development and flowering the following spring.  Use a hand pruner to cut off dead flower heads down to a pair of leaves, or use a hedge trimmer for larger plantings. Shear lightly, taking off only the dead flower heads.

The common French lilacs (Syringa vulgaris cvs.) produce  the largest flowers on stems that are not more than 5 or 6
years old.  Older stems only produce small flowers. Renewal pruning allows more light throughout an older plant and encourages new stems to grow and flower.  Lilac stems can grow very large and tree-like and they will tend to shade out new growth at the plant base. Use a lopper or hand saw to remove a third of the thickest stems at the base. Do this every year until all large stems are removed. You may still do this type of pruning now because the plant is still dormant. 

Rejuvenation pruning is a techniques that lilacs respond to when they are healthy, but are not blooming or are seriously overgrown because pruning has been neglected. Cut the entire plant back to within 6 to 12 inches of the ground as new growth begins in late winter prompts mature lilacs to send up many new shoots.  You may still do this type of pruning now because the plant is still dormant.Because lilacs bloom in early spring on the previous year's growth, rejuvenated plants won't bloom the first
year after this drastic pruning.