I can kind of help as I lost my dad five years ago. As someone above said the best thing to do is something you know they would enjoy. Or maybe something the two of you used to do together that will help bring back some happy memories. I'm not sure your situation but I usually visit where my dads ashes were placed in the cemetery. For me it's just nice knowing that's his final resting place. If you have any siblings try and do things with them especially if you are the oldest. Overall just try to enjoy the day while keeping all the wonderful memories in your mind. Getting upset is nothing to be ashamed of either, it's hard losing a parent, but always remember they would be proud of you no matter what.
I don't know how long ago you lost your mom or how old you are, but I lost my dad when I was 15, I'm about to turn 21. I have gone through many ups and downs since then. If there is anything you ever want to talk about feel free to PM, I know how hard it can be.