Example 1 demonstrates Inside Picking using 1 note per string. We play the first note with an upstroke and the cross over to the next string and play it with a downstroke. In this example the pick jumps over the string it previously played to the next string, then jumps over that to return to the lower string. With Inside picking you jump over the previous string to get to the next.
Example 2 demonstrates Outside Picking using one note per string. The first note is played with a downstroke and the pick continues to travel past the next string and changes direction to play it with an upstroke, it then travels past the lower string and changes direction again. With Outside Picking you jump over the next string before playing it.
Examples 3 and 4 are a 3 note per string pattern to be practiced with both types of picking. Example 3 starts with a downstroke and uses outside picking to approach the notes played on the high E string. Example 4 starts with an Upstroke and uses Inside Picking to approach the notes played on the High E. The goal is to be able to cross over to the next string without accidentally picking the former or latter while making the jump. This is difficult and requires a certain amount of looseness in the wrist. At first you may feel like your picking hand is bouncing all over the place with the outside picking so get your thumb joint on your picking hand involved and use it to retract the pick a tiny bit while crossing over strings. A move of one millimeter can make all the difference.
Example 5 demonstrates how Inside and Outside picking breaks down while using strict alternate picking on even amounts of notes per string. The first string change uses an up, down Outside Picking motion while the string change that repeats the sequence uses up, down in an Inside Picking motion. The same thing would apply to patterns of 4 notes per string, 6 notes per string etc.
Next we have a descending, three note per string sequence in Example 6 and 7. The left hand pattern remains the same for both exercises, the only difference being what pick direction each sequence starts with. Example 6 starts with a downstroke and will result in Inside Picking whereas Example 7 starts with an upstroke and results in Outside Picking. Which one feels more natural to you? Is the Inside Picking technique cleaner and faster or is the Outside Picking easier? Whatever your answer is, it's probably best to practice the more difficult technique at least twice as much as the one that feels more comfortable for now. Also, try doubling up the sequences to build up speed and help memorize the patterns if they are new to you.
Examples 8 and 9 use the same sequence in an ascending format and are to be practiced with Inside and Outside picking as well. That first fret to fifth fret pattern is a bit of a stretch, keep your thumb behind the neck, somewhere around the middle to help spread those fingers out. Again, try doubling up the patterns once in a while.
Example 10 is a long sequence in the key of G that is designed to combine both Inside and Outside approaches with string skipping. The string skipping presents a new problem to the realm of Inside and Outside Picking considering that you are now trying to jump over an extra string to make it to the next. It's easy to get sloppy on this one, try not to let it happen. Does outside picking make string skipping easier to you at all? Do you find that you end up hitting the string you are supposed to skip with Inside Picking? Pay close attention to these things, troubleshooting is an under rated ability amongst musicians.