Here's some info on sewing on silk, but would also work for just plain slippery fabric.
Use a Universal needle suitable to the weight of your fabric. However, very fine silk fabric may require a "sharp" needle. Sew a test seam to determine the best stitch quality. Generally 8-12 stitches per inch will be best. Again a test seam is the best way to tell. Being a natural fiber, silk does not dull needles as quickly as synthetic fabrics. However, you should still consider starting with a new needle.
The slippery silk fabric that was difficult to cut out may also be difficult to sew. You might try laying the fabric on top of strips of tissue paper and sewing through all layers. Some seamstresses have had luck using adding machine tape or even toilet paper as a support. These can be set in your lap and unreeled as you sew. Should the silk fabric tend to poke down into the hole under the presser foot, consider using a single hole throat plat or create your own by putting a small piece of tape over the opening. Sew a few stitches to make a nice hole in the tape, then sew through a scrap of fabric to clean any sticky residue from the machine needle.