How to Train Kittens to Stay Off Kitchen Counters. Part of the series: Puppy & Kitten Care. You can train kittens to stay off the kitchen counters by always feeding them at floor level and placing a carpet runner on the countertop surface when you have to leave the house. Keep your kittens earthbound with the help of this free video on puppy and kitten care. Read more: http://www.ehow.com/video_8405847_tra...