I have a cheap softwood workbench from Home Depot, and I stick a 1/4 inch dowel into a bookshelf at one end of the bench. Since my carvings are generally small, I stick a straight pin in the bottom of the carving, tie a piece of thread to it, and after wrapping the other end of the thread around the dowel a couple of times, secure it with a clothespin. This allows the carving to hang above the workbench. Using acrylics, I rarely get any drips.
For larger carvings, or those I finish with oil-based varnish, I just put a couple of toothpicks on the work bench and set the carving on the toothpicks to dry.