I have decided to write on techniques for cutting paper. Below are four very useful tools: scissors, a knife, a dry ballpoint pen (yes, dry pens are good for something), and a ruler.
clean straight edges
In the absence of a paper guillotine, a pair of scissors makes the cleanest and straightest cut. Use a ruler and the dry ballpoint to draw a guideline: the pen leaves a scored line but no pencil to erase later.
clean curved or intricate edges
Try a knife of some kind (with several layers of scratch paper underneath, to protect the desk). Mine doesn't look very artistic, but it works well. If (like me) you can't draw curved guidelines perfectly the first time, mark them lightly with a pencil. I used the knife to cut out the sides of the trunk and branches of the tree in once & now too, and then I tore the ends of the branches out. I also used the knife for the window and crenellation on the tower in I will say of the Lord. For the crenels, I cut four parallel slits to make five tabs and then folded two (every other one) to the back without cutting them off, because cutting tiny right angles perfectly is rather tricky.
soft straight edges (above, right)
Use the ruler and dry ballpoint to draw a guideline, but instead of cutting with scissors, carefully tear along it. If the paper is thin enough (such as the white cotton paper in happiness), the ballpoint itself may tear it.
soft curved edges (above, left)
Mark the beginning and ending points with the dry ballpoint, and then slowly and carefully tear between them. Some cardstock and other paper has colour or design only on the outside and a white core, as it were. If you want the white to show, peel the scrap piece up from the right side of the piece that you want; otherwise, peel the scrap piece down.