Before relighting your wood wick, make sure you have removed the blackened wood. The latter is composed of the ashes of the wick. However, the candle will not be able to relight without removing this small part. Use the beveled scissors to cut the wick or a handkerchief then pinch the blackened end.
You may have to light the wick several times before the wood ignites. It's a bit like a campfire. You have to give the wood time to catch fire. We advise you to tilt the candle slightly and light it with the lighter, holding the flame on the wood wick for a few seconds.