Question About Authority

I know that using the phrase "experts say that," is the anonymous authority fallacy. I was wondering, when using someone's statement as evidence for a claim, is there any standard to determine who is a legitimate expert?

There is no standard, per se. Your example would be an example of the anonymous authority fallacy (who the hell are these "experts"). When you cite expert authority (which is not in itself, fallacious) then one must take into consideration:

1) the level of expertise of the source
2) if the source is really an expert in the given topic
3) the way the response is phrased.

For example, the following go from most fallacious to legit.

My grandmother says that chicken soup is great for colds, therefore, it must be.

My doctor tells me that exercise keeps the immune system strong, therefore it does.

My doctor tells me that exercise keeps the immune system strong, I trust his advice.