Arpeggios are hard. Most people don’t enjoy learning them, but they are critical if you want to understand how to improvise over chord changes. It’s important to be able to find chord tones on the guitar and arpeggios are the best way to do that. Dominant 7 arpeggios are a good place to start because secondary dominants are so common. If you know your C scale and the E7, A7, and D7 arpeggios you can easily play over All of Me, for example. Take a look at these fingerings for dominant 7 arpeggios. If you have already learned these major scale fingerings, you will notice that the arpeggios come out of the scales, based off of the 5th. A great way to learn these fingerings is to play a C scale and then play the G7 arpeggio that is found within the scale. Just leave out the C, E, and A notes. Once you are fluent with dominant 7 arpeggios in all keys you can start learning some other arpeggios such as Maj7, min7, min7(b5) and dim7.
I am using arpeggios in my playing all the time, even when I am not playing them straight up or down. When I am playing chromatically, I like to start and end my lines on chord tones. The arpeggios that I have practiced form an underlying structure over which I build my linear ideas. This is true for all styles of music, not just jazz. There is a difference between choosing a scale that sounds good with a certain set of chords and choosing notes to target at particular structural points in a chord progression. Finding those chord tones can actually free you from the confines of a particular scale.
Good luck practicing your arpeggios, and have fun figuring out how to apply them creatively!
Alex Anest 