I think when used as an adverb or adjective, the word should be really, as in “She is really happy.” Real is equivalent to true, or genuine, or actual whereas really is equivalent to the word very.
Is it correct to use real as an adverb or adjective in this way?
We (i.e. the creators of Pain in The English) developed a series of iPhone apps to teach preschool kids how to recognize letters and words. (My wife developed the characters and I did the coding.) Our own 4-year old daughter has been enjoying them. They are now available on Apple's App Store. You can search for "bitskis" on your iPhone, or visit the official website at bitskis.com.
If you have kids and own an iPhone, please check it out. It's $2.
The objection to the adverb “real” is that it is informal, and better suited to speech than to writing. Some have gone so far as to object to “real” as an adverb entirely. This is one of those nineteenth-century grammatical shibboleths that is largely ignored in practice, and rightly. True, the adverbial “real” is perceived—by some—as less formal than “really,” but it is not incorrect. It has a long history of usage, both spoken and written, and is perfectly standard English.
“Real,” as an adverb, is a simple amplifier, similar to “very.” The adverb “really” is more nuanced; it might mean “very” (he is really angry) or it might mean “actually” (he is really angry). In general, however, “really” is more often used to mean “actually” than “very.” Whether “real” is the appropriate adverb depends on the intended meaning.
…or to quote Ren & Stimpy, “happy, happy joy,joy”!
The idea that that “real” as an adverb might have a certain nuanced difference in meaning from “really” hadn’t occurred to me before. Interesting; I’ll have to think about that.
If you’re looking for a hard “rule” though, I recommend you confine your use of the adverb “real” to colloquial language and stick with “really” in formal spoken/written English.