A. Remove all empty hangers putting all wire hangers and all broken/bent/weak hangers in a paper bag to be thrown away as you touch them (keep bag nearby and touch each hanger only once).
B. Place good empty hangers on your bed, dresser or empty box. (You should now have a tiny bit of room in your closet to maneuver a bit.
Notes: If you only own wire hangers go out and buy as many plastic hangers as you can afford. Not the flimsiest version but they don’t have to be very expensive. It’s nice to have a variety of styles. The smooth ones with a large opening and some with notches to keep spaghetti straps from slipping off. I also like to use about 10 of the felt covered non-slip type for things that tend to slip off (they used to sell them at Costco) I do not like to use them for everything though, it’s too hard to remove garments.
If you don’t have any empty hangers you can start with Step 2 but will need a nearby bed to have space for sorting, so don’t start close to bedtime or you will be moving a pile of clothes to get into bed.