A simple example... if you have a Major C, or even a C7, on the chart, you can play the triad a full step up: D, F#, A. This gives you the b5, the 13 and the 9.
If you play the 6th major triad over a root( e.g., A, C#, E over Cmaj), you get the 13th, b9 and the 3rd.
If you take the tritone of C and play that triad (F#, A#, C#), you get the b5, b9, and b7. A good dominant run could involve alternating between the triads of C and F#.
It sounds more complex than it really is. It's just putting a shape you already know over a chord you already know. Experiment to see which work and how. You can use it with comping or building solos.
I will be experimenting with different triads over chords to see how they work together.