Unless it isn't recommended for that particular recipe, I generally refrigerate my cookie dough before rolling it out.
I roll out onto a non-stick silicone mat, but you can use wax-paper. And I place a sheet of wax paper on top of the dough, too.
You can buy dowels at the hardware store - they are a great way to ensure that you roll out your dough to an even thickness.
Then pop the cut-outs into the fridge or even the freezer for about 15 minutes.
I don't have many baking sheets, or a very big oven, so I put cut-outs on wax-paper while I'm waiting for the cookies to bake, then slip the whole sheet onto a baking tray when one comes out the oven.
Bake at the recommended temperature, and set your oven timer! Cookies bake fast, and there are countless times that I would have completely forgotten that I had a batch in the oven if it weren't for the timeous reminder of the timer!
Leave your cookies to harden and cool slightly before transferring to the cooling rack, just so that they are not too delicate to move. Let them cool completely before icing.
If I'm not flooding them shortly after baking, then I store the cookies in Tupperware with paper towel between the layers.
The paper towel also absorbs some of the surface grease, which should help to prevent fat spots leaching into the Royal Icing.
If it is a particularly high-fat cookie, then I put new paper towel between the cookie layers the next day. This is also really helpful in humid summer when nothing dries out as quickly as you want it to - especially cookies and Royal Icing.