There is, of course, no easy way. It all eventully comes down to avid but critical reading. The more you read, the more readily you will distinguish dreck from brilliance. You will see dialogue that operates on multiple levels, dialogue which makes an emotional connection with the reader, dialogue that turns the course of the story. You will see dialogue used as a clumsy substitute for unobtrusive, timely exposition, you'll see dialogue that could have been better served with a quick sentence of narrative, you'll see flat attempts to make speech patterns expose quirky character traits.
You should definitely enrich you internal dictionary. There is endless amount of possible variants how to replace such boring words as say, tell, and ask. Just exert a little bit more efforts!
The later Spenser books by Robert Parker are beautiful examples of dialogue honed to a razor's edge. The first Spenser novels, written in the 70s, were verbose and dense. As Parker - and his readers - became more and more comfortable and familiar with the characters and their habits, though, he pared them down until he could tell a taut, satisfying story in a couple of hundred pages that could be read in a couple of hours.
Well, to use OP's example: "Blah blah blah", she says. "Blah blah blah", he says. "Blah blah blah" "Blah blah blah", he replies, scratching his head. "Blah blah blah", she answers, patting his shoulder. "Blah blah blah". "Blah blah blah", she yells, followed by a giggle. As I have done above, sometimes cut the added stuff. We know that these two characters are the only one there, so you don't have to show which is talking until one does something important, one leaves or a third party comes in.
