Here are a number of useful tools and technique for safely and precisely working with cardboard.
Consider getting a cutting mat before you start slicing up cardboard on your floor/desk/dining room table! You can use a layer of newspaper or magazines if you must, but a proper cutting mat will protect both your table top and avoid dulling the blade.
Most cutting mats also have handy rulers, guides, grids, and angles printed on them. They come in a variety of sizes.
Metal rulers are best, as they prevent blades from cutting into the edge, or even traveling up and over, as can happen with wood and plastic.
To help you create parallel edges, a square of some kind can be a big help. If you have one straight edge to begin with, you can create perpendicular lines from there with a square.
Angle rulers and protractors can also be very helpful in making precise shapes at particular angles.
It's good practice to measure and mark where you intend to cut before doing so. Have a variety of pencils and pens on hand.
One of the first things you'll need to do with cardboard is to cut it down to a useful size and shape for your needs. Utility knives and hobby knives are best, as they have very sharp, replaceable blades. Cardboard dulls edges quickly!
Other knives that work well are contractor's knives, for thicker cardboard and scalpels for curves and more intricate work. Both of these types also use disposable blades.
Here, a small straight edged metal ruler is used with a hobby knife to make a nice, straight cut.
Scissors work well, too, but again, they can get dull from too much cardboard use, so you may want to designate an inexpensive pair for cardboard cutting, and know that it may need to be replaced periodically depending on how much cardboard crafting you do.
For most straight cuts you'll want to run the blade alongside a metal ruler or straight edge to prevent it from running off the line.
A more specialized tool you should consider if you do a lot of cardboard cutting is a rotary cutter. It looks like the smaller, sharper sibling of a pizza wheel, and is usually used for fabric cutting.
Again, run it alongside a straight edge or else you risk the cut curving off the line.
To mark circles for cutting you can use a compass, a circle template, round object to trace such as cups and containers, or you can use a thumbtack and a loop of string or yarn!
One advantage of using a compass or the pushpin and string method for drawing your circle is automatic center hole!
You can then use the center hole for an axle, such as a bamboo skewer.
To help you make bends in cardboard, you may want to crease or score, one side of the material. For this, you can use a variety of tools. A dried out pen, a knitting needle, or a pointed dowel (not too sharp) all work well.
You will also want some tools for poking holes in cardboard. For this, an awl works very well, but you can substitute a bamboo skewer, toothpick, or small Philips screwdriver.
Crease to Bend
Run a creasing tool across the cardboard a few times in order to create a better bend.
A single hole punch is great for making holes in cardboard. You'll be limited by the "throat" of the tool by how far in from any edge you can punch. If you have very specific needs, there are specialized hole punches available at craft/hobby stores that have farther reaches, a variety of diameters, and different shapes of punch.
You can create freehand curves, trace objects, or use a flexible curve ruler. This is especially useful if you need to create multiple instances of the same curved shape.