If you are using peppermint leaves, I would suggest that you chop them up and sanitize them in vodka or Everclear. You won't need much, just enough to cover the leaves. I don't think you need to dry them first, just soak them for an hour or two and add the entire tincture to the secondary (if you use one) or the primary after fermentation is complete. Be careful though, peppermint can get overwhelming in a hurry. Add a small amount, wait a few hours and taste. If you need more, add more. It is easier to increase but impossible to decrease without brewing another batch and blending.
I make a Peppermint Pattie Sweet Stout and use peppermint extract since the peppermint is already a sanitized tincture of peppermint and alcohol in the bottle. That way i can easily add small amounts to adjust for taste. My friends all love the beer! As a matter of fact, I took a growler across the street to one of our neighbor's parties a while back. She gave everyone a taste and then cradled the gowler under her arm for the rest of the night so she could finish it! Her husband and I still chuckle about that!
One other note. If you keg your beers, your serving line may become impregnated with the peppermint flavor, especially if you are using vinyl lines. I have had that happen so I keep a separate line for the peppermint stout and install it when this beer is on tap.