Buying secondhand cashmere sweaters is a hobby of mine. Ebay is a great resource and thrift shops have some great finds. A few weeks ago I found a really nice full length tan colored cashmere skirt with the tags still on (!) at Plum right here in Beverly. Plumconsignment.com
I cut the pieces with the straight of grain running vertically. Then I sew the ends together to make the length I want. I have to make another length and then I sew them right sides together all the way down both sides to make a tube. I like to turn the scarf right side out and then serge the ends together and add decorative trim. The trim adds body which helps the ends lie flat against my body. I like to make the scarves long enough to go round my neck several times.
Hint: if you cut your lengths across the width of the sweater or skirt your pieces will curl and misbehave.
Another option is to make an Infinity Scarf.
Do everything the same way until the part where you would have added the trim. Sew by hand the ends together neatly so you have a circle. See the blue and gray one in the picture. For a more professional (read persnickety) effect leave about 4″ on one side near the end open and sew the ends together with the ends right sides together. Then turn right side out through the 4″ opening and neatly hand stitch the opening closed. This makes a continuous loop to wrap around your neck a few times.