If you don't get to know your instrument, you can't really tell how to work it. The long thin part is the neck, with the fretboard on the front. Each of the lines across the fretboard is a fret. At the top of the neck is the head and the tuning keys. Below the neck, is the body. The pickguard is a plastic piece next to the soundhole (the hole on your guitar). At the end of the strings is the bridge. Make flash cards with all of the terms for the guitar parts and test your kid by asking him where parts are.
If an instrument isn't tuned right, the notes will sound weird and the piece will fall apart. This is what the tuning keys--the flat knobs at the end of the guitar--are used for. One of the fastest ways to accomplish this is with a guitar tuner, but you can also do it by ear. The Justin Guitar website includes notes to tune your guitar to. Play the note on the site, and adjust the key. If the string sounds higher, it is sharp and needs to be loosened; a lower-sounding string is flat and should be tightened.
The strings on the guitar each have a name corresponding to the note it plays when none of the frets are depressed. These are "E," "A," "D," "G," "B" and another "E." These are hard for even adults to learn, but that's where a mnemonic comes in handy. For example, "Eddie Ate Dynamite, Good Bye Eddie" is a mnemonic to help you remember which strings are which in order. Come up with your own mnemonic with your kids.
Each time you pluck a string on a guitar, it plays a single note. A chord is a collection of notes that sound good together, and you usually play them by holding down several strings on the fretboard and plucking all of the strings at the same time. Help your kids find a chord to play, and show them which strings to hold down. Some chords may be hard for kids to play, and practice may be frustrating, but help your kids push through these frustrations.
Locate some songs you both enjoy and think will be simple to learn. Learn the chords that make up that song, and then practice moving between each of them. This will build what is called "muscle memory;" your hands actually remember the places for the chords. Shift between these chords in order, and play through the song slowly. Practice this song, getting quicker and faster each time. Eventually, play it over a recording of the song, and practice until you have the tempo and sound done correctly.