Basically, economy picking is alternate picking, the only difference is the way you change strings. Play the three note per string scale in Example 1 to get a feel for it. The picking hand is going "down up down, down up down" changing strings with the same picking direction. Same thing applies to example 2, descending with the opposite picking direction. This makes all the difference in the world. Watch guys like Tal Farlow when he's playing an up tempo tune and it looks like he's dragging his hand all over the strings, like he's "wiping" the notes out. This is also the method Frank Gambale uses.
The trick with economy picking is odd number note groupings. Any pattern with 1,3,5,7 etc. notes per string will allow you to change strings picking in the same direction, thus saving you from alternate picking hell. Examples 4 and 5 are an A major scale in note groupings of 7. This is a John Petrucci Style lick that can go by in a flash. When playing these odd note groupings it is important to practice with a metronome. The accents are all over the place and unpredictable so it can be easy to lose track of where the "one" is if you're not careful.
What about pentatonics? Good question. Pentatonic scales usually lie on the fretboard in two note per string shapes, an even number. how Eric Johnson can play these the way he does has always baffled me. Anyhoo, remember the "Extended Pentatonics" lesson I posted earlier? Changing the scale to three notes per string helps get the economy going. Example 5 is a pentatonic lick in E minor using economy picking and a five note grouping. Remember the metronome! These odd numbers aren't what we are used to hearing in western music, keep the rhythms tight.