How can you cure hemorrhoids without taking medicines?

Fiber. Try a high fiber diet, consider supplementing with a powdered bulk-laxaative such as metamucil.
FIBER. Hemorrhoid disease is often a byproduct of straining with defecation. Therefore, most people with hemorrhoids will benefit from increasing their fiber intake to 25-30grams/day and drinking at least 8-10 cups of water. Furthermore, it helps to "take the library out of the bathroom": get in, get out!
Fiber/bath/donut. Agree with the high fiber diet 20-25 grams. Should also consider stool softeners, sitz baths 3-4 times per day and over the counter meds like preparation h. Use an air inflated donut for sitting.