Pay attention to the specific words your children use to describe situations. If they say, "I hear you," that indicates an auditory learner. If they say, "I see what you mean," that indicates a visual learner. If they say, "I feel the same way," that indicates a tactile learner.
Note what your children do when they talk. Chatterboxes who tend to interrupt others may be auditory, quiet children who tend to daydream during long conversations may be visual and those who cannot talk without using their hands may be tactile.
Talk to your children about memories, paying particular attention to how they express them. An auditory learner remembers conversations and people's names, a visual learner recognizes faces and places more than events and a tactile learner recalls activities. For instance, from a museum trip, an auditory learner recalls the guide's explanations, a visual learner remembers the exhibits themselves and a tactile learner remembers the area in which kids could dig for dinosaur bones.
Ask what process the children go through when they try to spell a word if they are old enough and observe how they read. If they sound out words and tend to read aloud, auditory fits best. If they try to see the words in their head and like to stop and visualize the action taking place in a book, visual fits best. If they spell out words on paper and generally only read stories with lots of action, tactile fits best.
See how well children follow different kinds of directions. If they respond best and remember what you told them verbally, it indicates an auditory learner. If they follow written directions better or need pictures for guidance, it indicates a visual learner. If you need to show them what to do in order for them to understand, it indicates a tactile learner.
Listen to them when they complain. Children who complain that others don't listen to them may be auditory, those who complain you are not paying attention unless you are looking at them may be visual and those who complain nobody understands them may be tactile.