Make it safe first, tidy second
Broken glass in an opening is a hazard before it is a repair. The priority is to stop anyone walking into the opening or handling loose pieces: keep people and pets out of the room, close internal doors, and do not try to remove a panel that is still held at the top.
Loose shards in a frame can drop without warning when a door is shut or a window is moved. If the glass is in a door or a low window, tape a temporary barrier across the opening rather than leaning anything against the glass itself.
Temporary cover, done properly
Cardboard or ply screwed or taped to the frame is the usual temporary measure. Tape it to the frame, not to broken glass. If the opening is exposed to weather, tape the top edge first so water runs over the cover rather than behind it.
Do not force a sheet of anything into the opening to wedge it — a panel under load can crack the remaining glass or damage the frame, which turns a glass replacement into a frame repair.
What to tell us when you call
The suburb, whether the opening is a door, window or shopfront, roughly how big it is, and whether it is currently open to the weather or to the street. A photo of the whole opening — not just the break — is worth more than a description.
Also say what the glass was doing: a bedroom window, a shopfront the public walks past, a balustrade. Those are different urgency levels and sometimes different glass.
Why the replacement may not be the same glass
The pane that broke was the glass that was there, which is not always the glass the location calls for. Where the opening is in a door, alongside one, or low enough to fall into, the replacement has to suit that location rather than match the old pane.
That is also why a maker cannot always promise same-day: common sizes in common make-ups can be quick, but a toughened or laminated panel made to a specific opening has to be manufactured.