How do I take a large living room with wall space into a DIY closet?

Look for some free-standing closets that you could line up against the wall. IKEA has some nice products and ideas. Alternatively, shop the thrift stores for vintage armoires or chifferobes, and paint them to suit your color scheme. Good luck!

IKEA has closet solutions that look like furniture.

Without knowing the height of the ceiling or what material it is constructed out of...if it is possible to attach anything to the ceiling, suspend curtain rods, and hang grommet curtain panels from them to hide any clothing storage behind the curtains.

If it is not possible to mount anything from the ceiling, or if you don't live a convenient location to an Ikea store, or have no vehicle to get the Ikea items to your apartment, then I would suggest to use room dividers to hide clothing storage behind them. Room dividers are lighter and therefore easier to move than heavy armoires.

Simple you-put-together clothing hang up racks (think of the ones on wheels that are used in retail stores) are quite readily available. These would offer you additional hang up space.

I like the idea of Room dividers made with louver Doors or other room doors that you can hinge together, stand them in zig zag pattern and put stuff behind them.. sometimes you see these at Garage sales or find a Habitat for Humanity Store... also look for old Ceder chests or Benches with storage in the seat.. or Dressers with deep drawers you can use for Storage. Raise you bed with those blocks you can make or buy and then you have room under your bed for the plastic tubs with lids so you can store out of season clothing like sweaters or summer clothes.. you can get as many as 4 Tubs you can just slide in under the bed from the sides and the foot..