You exhale during the hard motion of the exercise, so if dumbell curling exhale during lifting it up, and inhale bringing it down. If you do that wrong you can develop hernia's where lifting heavy weights your intestines can come at you anal.
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You're supposed to exhale during the concentric phase, i.e., the harder part. It is often better, however, to hold your breath (or more correctly, utilize the Valsalva maneuver), during both phases. This generally allows you to generate a little bit more force, but it takes practice.
This is an evolutionary mechanism that humans have developed, in fact, and it becomes obvious when you think about it. I believe it is Mark Rippetoe who gives the example of having your car run out of gas in the middle of an intersection, requiring you to push it out of the way. Imagine how you would go about this: you would take a big breath and hold it before giving it your biggest push. It is innate.