Simple, but weird.
All you do is add water to corn flour (sold in some places as corn starch), aiming for a ratio of approximate 2:3 of water to cornflour.
You can do this on a small scale, say in a cup, and it will be interesting. But if you can, we recommend a rather larger quantity. We found kg bags, for a few dollars each, at a local Asian food warehouses.
Take your time to mix the water in, as the components act bizarrely, even at this stage, with the spoon slipping across the surface unless you mix very slowly.
When a force acts on the mixture, e.g. if you try to mix it quickly, it acts like a solid. But if there is only a small force acting, e.g. if you mix slowly, the mixture will act like a liquid. So you can pick up a piece that feels like a solid lump, but if you try to hold onto it, the mixture will become liquid again and drip off your fingers.
The viscosity increases with force. A fluid that behaves like this is described as a non-Newtonian shear-thickening fluid, or a dilatant fluid. A 'normal' (or 'Newtonian') fluid has the same viscosity (flow) regardless of the force applied.
You have probably also encountered a shear-thinning non-Newtonian fluid. These are mixtures that become more fluid (less viscous) when a force is applied, and toothpaste is an example – that is how you can get it out of the tube but it doesn't drip off your brush.
Its been difficult to find an explanation for what is actually happening. The closest I found was by RP Chhabra here. Apparently the spaces between the starch molecules are filled by water when there is no/small movement. But when a stronger force is applied the molecules expand ever so slightly, such that the water is no longer sufficient to fill the spaces, and then the friction between the starch molecules becomes more significant.
There is also an analogy to a snow plough here, which compares the increased resistance to the way snow builds up in a solid pack when you push into it.
PS When you're done, don't tip this down the drain…