Cuttings are not usually the best way of propagating lilacs, and despite what some written sources say I have not found them to be especially easy to root (although obviously there are lots of woody plants that are even *harder* ). Best advice I know of is to take softwood cuttings in June or so, after flowering. You want about 8" or so; bend the branch and see where it snaps naturally, then tidy up the ragged end. Dip in softwood rooting hormone, pot up and keep humid and out of direct sunlight like you would for any cutting, and hope for the best. I suggest doing a *bunch*, in hopes of getting *any* to strike.
Unless your lilac is grafted, though, you can usually find rooted suckers to dig up. Even varieties that don't "really" sucker still seem to produce very short localized suckers IME.
Or, you can try rooting a small lower branch by bending it to the ground, wounding the lower side somewhat, then pinning it to the ground iwth wire or a rock, mound good soil over it, and leave it that way til next year at which time there is a good chance you will discover it's rooted and can be severed from the parent plant and treated as a new plant on its own. This can be done even on grafted lilacs. Again, I suggest "vote early and often", as not all of your layers will take.