Step 1: Strike self on forehead.
Step 2: Say "Oh, crap!" (feel free to be creative here by substituting the term "crap" with another term such as "shit" or "fuck". NB: avoid terms that might be construed as having racist, sexist, or classist connotations, as you already know your privilege cluelessness. Keep it simple to avoid an iterative loop.)
Step 3: Say "I'm such an idiot for not seeing that before!"
(Optional steps 3B-3C may be initiated by member of relevant minority saying, "Well, that's because you're privileged and didn't have to think about it before." In which case, you may respond by saying, "augh! I know!")
Step 4: Say "Now I know better. I won't do that again."
Final step: KEEP THE PROMISE YOU MADE IN STEP 4. This requires you pay more attention to the oppression of people different than you. However, by noticing your privilege once, you've demonstrated you can do it again. So, practice.
(This public service announcement brought to you by a recent moment of recognizing my white privilege.)