Here is a video where I show a Jesse McReynolds cross-picking exercise I have found very helpful. The right hand strokes for the beginning example are DUUDUUDU. D means downstroke, U means upstroke. If you watch my right hand in the video you will get the idea.
I play a D chord with my 3rd finger on the 7th fret of the G string, my 1st finger on the 4th fret of the D string. Then I am leaving the A string open for effect.
Walking my 3rd finger down from the D note to a Db (6th fret) makes a Major 7 sounding chord.
Then walking it again down a half step to a C (5th fret) has the notes C, F#, and A this makes for a D dominant 7 sound often notated as simply D7. D7 pulls to the tonic of G.
This simple progression is used in many songs including Dylan’s, “Simple Twist of Fate,” as well as the song, “Waste,” by Phish. Try this same trick down a string set using the open E as part of A, Amaj7, A7, D chords respectively.
At the end of the video I play a tune, Sugarfoot Rag to show how different cross-picking patterns can be used within one tune. Start with the simple patterns more will be introduced in later lessons like alternating DUDUDUDU.