Clean the wainscot by wiping it down with a damp sponge soaked in warm water and a mild detergent. This helps remove dust and debris that interferes with caulk's ability to bond properly with the wainscot. Let the surface fully dry before continuing.
Apply a primer over the wainscoting with a sprayer or paintbrush. This further helps the caulk bond to the wainscot. An oil-based enamel undercoater works well for this purpose.
Hold the tip of a tube of acrylic caulk to the cracks in question and slowly squeeze the trigger of the caulk gun to release a slow, steady stream of caulk into the cracks. Allow the caulk to dry overnight.
Sand the caulk down with fine sandpaper to make it smooth against the wainscot surface. The wainscot is now ready for painting.