Look at the score you are using to perform, it's possible the composer's dates are located in the preface or elsewhere on the score.

If you can't find dates on your performing score, a good place to look is Grove Music Online. 

A third option is to look using Google, but be sure to find a website that has been updated recently and has verifiable authorship.

If you're having trouble locating a composer's birth and death dates, contact the Music Library at lib-mus@uiowa.edu.