I found there are mainly 4 ways to stiffen a project. All four can be applied by a soft clean paint brush. The homemade stiffeners can be washed out, so if you make a mistake, wash it and start over. For any shaped product, find a similarly shaped object, cover it so it won't get wet and insert it in the bowl, basket, box, etc. to obtain the desired shape.
The first is specifically meant for using on clothes as a spray starch but can be used for fabric projects. It's a simple process:
Heat 3/4 cup of water in the microwave until very hot (boiling if you're doing it on the stove). Mix 1/4 cup cool tap water with a tablespoon of corn starch and mix well. Slowly add the corn starch mixture to the hot water. Wait until it cools and pour it in to a spray bottle to use while ironing. Cautions on this method: Solution will only stay good for a couple of days. Don't use it on items you intend to store since it may attract mildew or bugs. To combat those problems, I may try to mix a few drops of Tea Tree Oil in the hot water prior to mixing. Tea Tree Oil is a natural germicide, fungicide, and bactericide.
Then there is the old fashioned sugar based starch a lot of grandmas used when ironing or making lace work. It's basically the same process but different ingredients: Mix equal parts sugar and water in a saucepan. Bring to a slow boil being careful not to burn the sugar. Immediately remove from heat and let cool to room temperature. Dampen your project and remove all excess water with an absorbent towel. Cautions on this method: Should not be used for permanent stiffening. Will likely yellow over time and may attract mildew and/or bugs. May get sticky in humid conditions.
Mixing equal parts white glue and water (use more water for more pliable projects) is another simple, quick way to stiffen projects.
The most permanent and durable method is to use one of the commercial fabric stiffeners on the market. Mix it according to the manufacturers directions. Caution with this method: It is permanent so follow the directions. Check your local craft store for brands.