Before starting a new project you should properly prepare fabric before cutting it by washing and ironing it. Natural fibers or fabrics with elastane can shrink significantly. Skipping washing fabric before sewing might result in garment shrinking in first wash and basically it can be ruined.
You need to wash fabric in a way it will be washes after it will become a finished garment or home textiles. With cotton, linen, viscose or polys you can wash them in washing machine with proper settings (30-40 celsius for colored linen/cotton, up to 90 for white cotton - in case of home textiles like washcloths). Machine washing will result in more shrinkage than hand washing and will soften especially linen more than hand washing will do. You can hand wash cotton and linen in higher temperature than wool and it can be wrung out the water and agitated more without much of damage.
I wash all of my fabric for clothing by hand, anything for home textiles goes into the washing machine unless it's some delicate fabric.
Wool needs to be either dry cleaned or delicately hand washed in cold water, with proper detergent, no agitation. Leave it to soak a bit. Heat and friction is what ruins wool the most. Leave it to drip off or roll it into a towel and delicately press it inside sink/bathtub - like with woolen sweaters.
Ironing fabrics, especially wools, can also be a way to prepare them before sewing, though it it was laying for ages at the store, it's better to wash it to get rid of dust or any stains. After washing your fashion fabric and drying it, you should iron it with settings for type of fabric you'll use on the wrong side, unless it's crinkle fabric. You need to be careful around velvet and iron it only on terrycloth towers to not make it matte. Silks and very delicate fabrics that need to be ironed on right side should be ironed through a cloth.
After ironing leave it for a while to cool off before cutting. Ironed fabric will ensure that pattern will lay smoothly and you'll be able to cut out pieces properly.
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