That's ALOT of information there for one lesson...but very cool and helpful stuff!
Just take it one line at a time...
Cmajor---c,e,g-------C major, C lydian (4th mode Gmajor)
Means when playing over a C major chord (which is based on C...E...G)
The scales that fit well over it are C major and C lydian.
Here's a very good site to help you see the scale on the fretboard...
http://jguitar.com/scale?root=C&scale=Lydian&fret=0&labels=none¬es=sharps
It would be good pratice for beginners to record yourself playing a C major chord for a few minutes with a click track, then play it back and alternate between the 2 scales (C major and C lydian) over top of it, so you can get a feel for how they work and why they work over a C major chord...training your ear is the most important thing as I musician IMO. It's cool to hear how moving one note in a scale (up or down) really alters the entire feel of what you are playing.
Then try moving on to the next line Ed posted...
C6------- c.e.g.a-----C maj, C lyd
...and so on.