You can wash silk at home and keep it looking new sans dry cleaner. Here’s how I take care of my silks from the comfort of my own laundry room:
In a plastic or enamel basin, fill with lukewarm water and a 1/2 cap of mild detergent (the one I use is linked below) and submerge your scarf. DO NOT use regular laundry detergent which will be way to harsh for the fabric. If you need to spot-treat your piece, apply some of the detergent directly to the affected area while the fabric is still dry and allow to sit for an hour prior to hand-washing.
For a few minutes, gently agitate the scarf in the basin. Drain the water and run the scarf under lukewarm water, until the water runs clear. Gently press out excess water making sure to not wring the fabric, as silk is more delicate when wet. Lay flat to dry on a drying rack.
Once dry, the fabric may be slightly wrinkled, so you can steam these wrinkles out to finish and return your scarf to its original state. Do not iron!