。
I believe diet therapy is more effective than medicine.
Literal
Medicine [than-より] diet-therapy [gen-の] side [subj-が] works [quotative-と] am-believing.
The comparison pattern X より Y の方が ('Y more than X') with 効く ('take effect, be efficacious') — here 効く is the medical sense. 食餌療法 (dietetics/diet therapy) is medical terminology: 食餌 is the formal word for 'food/diet' (note the obscure kanji 餌 for 'food, bait'), 療法 is 'treatment method.' The ~と信じる ('believe that X') uses the quotative particle と.