One of the hardest things about grammar is those damn hyphens. I have an entire style sheet from Chicago Manual of Style just on hyphens and every situation in which you do and don’t use them. I won’t even attempt to try to “teach” them to you.
But there is one DON’T that’s easy to remember. The -ly form of an adverb is never hyphenated when used in conjunction with another word to modify something. For instance, heavily medicated patient, not heavily-medicated patient. I could attempt an explanation of why this is (and probably make it understandable, even) and if anyone cares, I’d be happy to, but in the meantime, phrases like the ones below, in the CMoS reference, and any other-ly adverb phrases don’t ever get a hyphen.
adverb ending in ly + participle or adjective: highly paid, utterly useless. (Open whether before or after a noun.)