In psychlinguistic research, practitioners use what is called dichotic listening technique whereby the subject under study receives different prompts through both ears simultaneously. The prompts played into each ear are different; therefore, the ability to recall prompts played into either the left or right ear determines dominance.

Reza's answer is correct. Other techniques include TMS and FMRI. Having said that, I must also tell you that the notion of right dominant vs left dominance for language has fallen into disfavor if not rejected altogether. It has always been a problematic concept in any casa, as both left handers and women were shown to be less dominant than right handed males. It's is difficult to sustain a theoretical construct that applies to less than half the population.

nice theory...can we collaborate?