How can I safely work in my attic without a floor in place?
What you have in your attic is blown cellulose or fiberglass insulation. It can be moved out of the way and replaced in small areas without too much harm to its insulating value.

To move around in your attic, you need to step only on the wooden framing members... virtually any portion of the truss rafters, or any of the boards laying across them perpendicular. You could also take some sturdy boards up with you and move them around as needed, laying them across between the trusses.

If you step between the framing onto the drywall you will tear it loose from the framing and cause serious damage to the ceiling below (and/or yourself). It's critical that you avoid doing so.