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One such site is Learn 2 Type for kids. Here you can sign up for a free kids account and get started on lessons. If your child is K-2nd grade, you don't need to sign up for an account. Instead, you can go straight to the Tots typing page.
Goodtyping.com is another basic lesson typing site that teaches touch typing. You can register and track your progress or not register and start at the beginning each time you go. This is a good site for the no-frills crowd.
So, if you're looking for some typing lessons these can at least get you started.