There are any number of ways of saying you're hungry.
I would disagree with your source that おなかがすきます is better than おなかが空いています. As you note, the later indicates that this is your current state of being; the former indicates that you will be hungry.
How you use it? You just say it. I'm not sure what you're asking. おなかが空いています is a complete sentence already. Nothing more need to be said to express the idea that you're hungry.
There are a number of other ways to say you're hungry.
おなかがへった
I don't know that this is as versatile as the one you offered. I only recall hearing this being used in plain form. I suppose you can also say
おなかがへっています
おなかがへりました
I don't feel like there's much of a difference between these two.
You could say
おなかがペコペコです
but I feel this is more like saying "I'm starving".
Regarding which is more appropriate in circumstances where you should be polite, I'm not entirely sure. My gut feeling (excuse the pun) is that it's always safe to go with おなかが空いています.
Along these lines since I've suggested both plain and polite forms with the verb へる, I should (per @chocolate's nudging) mention that beside すいています etc, you can also use the plain form:
おなかがすいた。
I heard from different sources that 'おなかが空きます' is apparently better than 'おなかが空いています', is this true?
-- Which source? Could you give us the link?