A prop master develops a prop list by reading the script. The director, designer, and/or stage manager may come up with their own prop list; you still need your own so you can get working right away, and so you can make sure the rest of the production team has considered all the props that may be in the production.
First off, if your script comes with a prop list in the back, don’t use it. These are from the original production. The design and direction of your production will certainly be slightly altered, and can even be totally different.
Read the script twice. The first time is for fun, to get an overall feel of the play. You want to be able to have an intelligent conversation about the play with the rest of the design team. You don’t want to be the one at the meetings going, “Wait, Juliet is a girl?” The second time you read through it is to start noting props. Have your own copy of the script so you can mark it as you read. This script should live in your prop bible. Mark the page number of the prop on the prop list for easy reference later.
You can find props references throughout the script. The scene descriptions will give descriptions of the set furniture and some set dressing. The stage directions will tell you what hand props are being used, and how they are used. The character descriptions can give more clues about hand props, and can also hint at possible costume props. Even the dialogue can hold additional prop notes.
Look for clues on how a prop is used, and what it needs to do. If a chair is introduced on page 3, and on page 42, a character leaps on top of it, that needs to go on your prop list. A designer will usually decide what a prop must look like, but it is up to you to figure out what the prop needs to do. The director will also determine what a prop needs to do in rehearsal, but it helps to know as soon as possible if anything on your list will take some time or effort to build or acquire.
One final bit of advice comes from Bland Wade, who reminds you to consider all the ramifications of a stage direction, rather than what is merely written down. When a script says a character enters “smoking”, you need to ask what kind of cigarette he has. Where did it come from: a pack, a cigarette case, a friend? Where do the ashes go? Does he light it on stage? With a lighter or matches? What kind of lighter? Where does he extinguish it? In an ashtray or the floor? One simple stage direction can lead to a page’s worth of props.