You can't discard Cellar to itself, since it isn't in your hand any longer when you resolve it. You choose what cards to discard and discard them all at once. You only draw cards after you have discarded. If you have to shuffle to do the drawing, the discarded cards will end up shuffled into your new deck.
In an article on Board Game Geek, Donald X. Vaccarino commented on the development of Cellar:
- The oldest version of this didn't give you +1 Action. It obviously needed it, got it early on, and survived unscathed since. 
Note: Strategy articles are not necessarily based on fact, but on players' experiences or simulation programs. Certain cards will be stronger in some set-ups and weaker in others.
- Cellar has a net effect of -1 card, so discarding as many cards from your hand is beneficial. 3 or more is optimal.
- Cellar works really well with other cycling cards, including terminal ones.
- Cellar works well in the end game to pass up dead cards like Victory cards and Curse cards.
- In the mid and late game, discard Copper as you may draw a better Treasure card.