The water should be a bit sudsy. Fold the wet garment into a shape that you can twist in your hands , then wring it out. Empty the sink and fill it with clean water Dunk the garment, swish it around, and wring it out again, using the important technique. Getting things as dry as possible at this point saves drying time, which can be pretty long, especially in damp weather. Hang it up.
Shirts do well on a plastic hanger.
Never use a wire hanger. Anything you improvise is probably all right, but be careful where you drip. They're tough to clean and worse to get dry. Polyester fleece is lighter and cleans up better than cotton sweatshirts. Dark colors, neutrals and prints disguise stains and wrinkles.