How do I add a video effect to multiple clips in my timeline at once?

Either combine the clips into a compound and apply the effect to that, or apply it to one and paste attributes to the others.

or... you can command click to select all the clips you want to apply the effect to, then double click the effect in the Effects browser. (PS - you can't simply drag and drop an effect on multiple clip selections, the effect will only be applied to the clip you drop it on -- but double clicking the effect will apply it to all selected clips at once.)