Learn Russian: Вы помогаете больным?

The verb помогать (to help) always takes the Dative case in Russian. Instead of "helping someone" (Accusative), think of it as "giving help to someone."

I thought больной was an adjective meaning "sick". Why does it translate to "patients" here?

In Russian, больной is often used as a substantivized adjective—a word that declines like an adjective but functions as a noun. When used as a noun, it means "a sick person" or "a patient." In the plural, it means "patients."

If it functions as a noun, why does it take the -ым ending in the Dative plural? Don't nouns normally take -ам or -ям?

That is the tricky part about substantivized adjectives: they keep their adjective endings no matter what role they play in the sentence. Since больной is grammatically an adjective, its Dative plural is больным, entirely ignoring standard noun endings.

How would this sentence change if I were asking about helping a single male patient?

You would use the Dative singular masculine form. The adjective больной in the Dative masculine is больному, so the sentence would be: Вы помогаете больному? (For a single female patient, it would be Вы помогаете больной?).