How do you reinforce fabric?

In order to harden fabric you need to use some kind of starch. The type is dependent on why you need the fabric hardened. For a low-level starch you can use spray starch and an iron (simply spray it on, let it soak in and iron it), for something a little more stiff use a commercial product (something like Plaid's "Stiffy") or a homemade starch solution (you can buy starch in the grocery store - you boil it in water and then soak the fabric in it).

Many commercial starches can be painted on with a paintbrush too. You an make a starch from sugar Boil 1/2 cup sugar in 2/3 cup water - let cool and dip the doily and shape and let dry-