When you learn a new scale it is a good idea to learn how to harmonize it creating arpeggios over it. You may be asking what that means. This is simply building a triad or seventh chord off of each note in the scale. Using these arpeggios gives you a wide range of arpeggios to use over your playing. When you are generalizing over a song you can pick any of these arpeggios or play the harmonized scale ascending or descending. Any scale can be harmonized.
Before you start to harmonize a Scale let me quickly go over the nerd stuff. The word harmonize comes from the word harmony. Harmony is the underlying progression of notes. Notice, I did not say chords. Harmony can be chords, but it does not always use chunks of notes. Harmony can be split up into broken chords (notes from a chord played individually.) If you want to harmonize a scale you need to build intervals of thirds. You can review intervals here. A triad is a 3 note chord (with all thirds) and a seventh chord is a 4 note chord (in all thirds.) So in brief, you need to add a couple notes to each scale tone using thirds.
Now if you are not generalizing over a chord progression you may want to approach this harmonization a little differently. Take the arpeggio and figure out which arpeggio belongs over the Third of the chord, 5th of the chord or 7th of the chord. This will allow you to focus more on important tones. You will be starting arpeggios on the root position arpeggio which is very connected to the chord. Below is an example of harmonized arpeggios.
Once you are comfortable with these 2 approaches you can intermix them in your playing for a unique sound and more option. The more options you have, but better you can play a wide range of music and have fresh and new ideas. Spend some time working on harmonizing scales and learning to play them. Once you are comfortable with that spend some time memorizing then harmonized arpeggios.
Using this same system you can start to imply altered tones in your playing by changing your arpeggio choices. You can learn to play extended arpeggios and just be freer with your music. These are not meant to restrict your playing; rather they give you building blocks to use to make music. It is hard to be innovative without knowledge of what came before; it is also hard to be good without the knowledge of the basic building blocks of what you want to do. Arpeggios and scales make up much of the music we hear. Learning to use them to our benefit is well worth the time.