Silks are washable, but always test a swatch first to be sure you like the results.
To test, I cut a 4-5” strip across the width of the fabric, and if it ravels, serge the raw edges. Then, cut in 3 sections and hand launder one piece, machine wash/cool/gentle on another, and wash/dry gentle on the last.
Fragile and embellished silks may require dry cleaning.
Silk organza is one fabric I NEVER machine wash/dry as it becomes much softer and wrinkled - though this may be a desired effect.
I sometimes toss silk taffeta in the washer/dryer, which makes it a bit more cotton-y, this kicks back the silky shine and creates lovely all-over crinkles. I take it out of the dryer when it is just a bit damp, smooth it out, give a light press. You can then sew and press as usual, and it will retain the soft crinkles.
After sewing, never put silk in the dryer again. Hand launder or wash gentle and air dry. I take silks out of the laundry while still very wet, hang on a hanger and pull and smooth the seams and hems, allowing the weight of the water to do the work, then touch up with an iron or not.
Cutting
Cut sheers and slippery fabrics on top of paper, squaring off the end to align the grain. Use tissue or pattern making paper.
It is ok to tape the paper together to get the width of the fabric. Place the pattern on the fabric, pattern pieces on top, then pin and cut through all the layers.
This keeps the shape of the pattern pieces so you can move them around to mark.
Mark with tailor tacks, snips or tiny dots with a dressmaker's pencil. I avoid using tracing wheel/paper as it can leave marks
Sewing
Make samples with scraps to see which combination of needle size and thread works best.
Sew with a sharp needle
You can use silk thread, but a fine long staple polyester thread is a good choice too
Test for iron temperature and whether the iron leaves marks if you press on the right side.