What is the most effective treatment for ADD and ADHD that excludes chemical prescriptions from a doctor? Besides chemical medications that are prescribed that can increase the level of dopamine, and other important neurotransmitters in the brain. What is the most effective natural treatment method for ADD, and ADHD?
Not much seems to work; psychotherapy appears questionable when the patients are re-evaluated by someone else. The only thing with a minor but generally applicable effect is free fatty acid supplementation, although the effect may be so minor as to have no clinical value.
Of course, most of these findings come from a meta-analysis (Sonuga-Barke 2013) published in a psychiatry journal...

Two different analyses were performed. When the outcome measure was based on ADHD assessments by raters closest to the therapeutic setting, all dietary (standardized mean differences=0.21-0.48) and psychological (standardized mean differences=0.40-0.64) treatments produced statistically significant effects. However, when the best probably blinded assessment was employed, effects remained significant for free fatty acid supplementation (standardized mean difference=0.16) and artificial food color exclusion (standardized mean difference=0.42) but were substantially attenuated to nonsignificant levels for other treatments.
CONCLUSIONS:
Free fatty acid supplementation produced small but significant reductions in ADHD symptoms even with probably blinded assessments, although the clinical significance of these effects remains to be determined. Artificial food color exclusion produced larger effects but often in individuals selected for food sensitivities. Better evidence for efficacy from blinded assessments is required for behavioral interventions, neurofeedback, cognitive training, and restricted elimination diets before they can be supported as treatments for core ADHD symptoms.

The editorial that accompanied this paper had this pull-out:

Behavioral treatments have been
demonstrated to be helpful for children
with co-occurring disorders and
symptoms, although this blinded
analysis did not show efficacy for core
ADHD symptoms.

And it's worded that way because a prior meta-analysis (Fabiano 2009) using less stringent criteria (no blinging required) found (of course) that behavioral interventions work.
Regarding food colorants, only about 8% of ADHD children are estimated by a different meta-analysis (Nigg 2012) to be affected/sensitive.
And a meta-analysis of diet interventions Pelsser 2017 was quite skeptical of most stuff:

Considering the small average ESs [effect size] PUFA [poly-unsaturated fatty acid] supplementation is unlikely to provide a tangible contribution to ADHD treatment, while further research is required for AFC [artificial food color] elimination before advising this intervention as ADHD treatment. The average FFD [Few Foods Diets] ES is substantial, offering treatment opportunities in subgroups of children with ADHD not responding to or too young for medication.

So the cool new thing is FFD now. Since the last paper is freely available... I won't say much more, except that it may take a year to permute food choices until the right few foods are determined. They do say in the (body of the) paper that (owing to this time-scale issue):

large-scale implementation of the few-foods approach would not be a realistic recommendation.

I have to wonder why that didn't make it into the abstract.