Your mat should be unrolled so that the edges curl down toward the floor. Line the mat up with those of your neighbours so that you help to create organized rows (unless you are advised to arrange in a different orientation).
“Props” are the tools you can use to help accommodate for anatomical differences in your poses (i.e., arm length, flexibility, etc.), and include blocks (foam or cork), blankets, straps or belts, and bolsters(pillows).
PHD Yoga do supply these but you are more than welcome to bring your own if you wish. If the teacher knows you are new to the practice, she will give you some guidance on how to use them, but the basic rule is that they should be used to bring more stability and easefulness to your poses.