To jimmy a door open (this is different from carding/shimming/loiding), you increase the gap between the door and the frame enough so that the latch/bolt and the frame no longer interact with each other. This works best on flimsier (particleboard) doors, set in wooden frames.
Do note that it is possible to damage your door doing this, and if you do, I, naturally, take no responsibility. Also don't break the law pls kthx.
(and please don't take notice of the fact that I'm doing this from the inside side of a door)
Step 1: Tools
To do this, you will need either an air wedge or a crowbar, with the air wedge being the preferred tool (smaller, lighter, doesn't leave marks, etc). An important thing to note is that, in my experience, air wedges work better in doors that open away from you, and crowbars work better in doors that open toward you.
Step 2: Wedging the Door
So, start by deflating your air wedge. Now, take your flattened wedge, and slip it into the gap in the door. You want it to be as close to the latch as possible, and with the door as centered as possible on the wedge.
If the lock on the door is a deadlatch rather than a deadbolt, it is probably a better idea to use the wedge to increase the gap just enough to disable the deadlatch, and then loiding the door open normally, rather than completely jimmying the door open (less chance of damaging the door).
Step 3: And Pump
and we start inflating the wedge...
Step 4: Open!