Be careful not to over mix your cookie dough. You are probably annoyed to continually read this in recipes, but it's true and it will result in a tough cookie.
Chill your dough...a lot. I chill my dough after I make it, to allow it to relax and chill at the same time. After rolling the dough, and cutting the shapes, I chill the cookies in the freezer, pulling them and placing them directly into the oven. If the dough becomes too soft while rolling, it gets another trip to the freezer.
I re-roll my dough scraps once and then toss them. Re-rolling your dough, is in essence, mixing it, and building the gluten, creating tougher not tender cookies.
Start with simple shapes. I know that really cool cookie cutter you got from grandma this year has been begging to be made, but if you start with overly complicated shaped, you will become frustrated. Try a heart or even a large flower first then work up to that piggy shape.
Watch bake time. There is a concept called "carryover cooking." You may hear it on cooking shows, often times in reference to meat coming out of the oven. Despite the fact that we are removing the heat source, the food removed from the oven is still hot, and will still continue to cook a bit, even after removal.
I read once that adding a bit of spelt flour will add a little crispness to your cookie, without making the cookie hard. I tried it in my sugar cookie recipe and it worked like a dream. If you want to try this, I suggested replacing a ¼ cup of the flour in your recipe with spelt flour and manipulate the recipe from there.