Read the play several times. The director and the stage manager mark places on the script where they want props. For example, if a scene calls for Betsy to escape from a burning room, you will need smoke.
Compile a list of props that you'll need for your show. Consider using an electronic spreadsheet to list your props so that you can sort your list. Pay attention to the smallest details. For example, if Betsy is thirsty and takes a drink, you'll need a glass.
Think of simple solutions for products. You can purchase many props such as glasses, plates, silverware and decorations from Goodwill, Salvation Army or a thrift shops. For smoke, you don't always need a smoke machine; buy dry ice from the store and place in water to create the illusion of smoke.
Call local theaters and ask where they purchased their props. Dinner playhouses are good resources as well.
Grab the phone book, or use the online version, and look under theatrical supplies or equipment for items such as smoke machines, backdrop rentals, and stage lighting.