Skype (and hr Internet in general) as a medium communication with a child is very different from a play in direct physical contact, and I feel that people around invented a number of little helpful tricks. For obvious reason, it is more likely that grandparents are involved in "distance homeschooling" rather than parents. Can anyone share his/her experience, not only at mathematical, but also at purely practical level, say, selection of visual communication hardware simple and flexible enough for use?
Skype usually has pretty good sound quality, so any setup works. I like simple one-ear headphones with a microphone, because it reduces the ambient noise people can hear on the other side.
One simple and pleasant thing to do is watch a short video together (each on your own machine), then discuss it in Skype.
Pre-literate kids like smileys and learn to make them before they learn to type text. Skype has secret smileys, which you can use to impress kids. That is, you can "code" a little picture that is not in the drop-down menu of regular smileys.
Skype does not have a built-in whiteboard, but you can go to a collaborative whiteboard online while talking on Skype, since it's easy to share a link.
Younger kids find touch technology easier for almost everything, especially things like whiteboards, where they can essentially fingerpaint if they have a touchscreen.
Which brings me to the next level of communication coolness. You can step together into a virtual world, like Minecraft, and keep voice communication going over Skype. Then you can build together or do other modeling, while you talk.
For a more one-sided version, you can screen share a lot of cool things that happen on your computer, such as Mathematica models. The only things that don't share over Skype well are fast animations or videos.