If your machine has needle up, needle down, I found this to be a godsend...needle down holds your fabric in place while you shift and adjust fabric to sew the next length.

As far as cutting, I flip my table pads over to the felt side so the fabric doesn't move and slide around while I cut the fabric.

I am a garment sewer and about to get into home dec so I will be following this posting for other helpful hints.

For slippery fabric you can pin it to tissue paper under the pattern and leave the tissue pinned to the fabric. The paper will tear out easily when you're done. If the pins leave hole in the fabric, try to keep the pins in the seam allowance.

For curtains you can use a strip just under the stitcing line.

My grandmother did a lot of her own lingerie, using a variety of sheer things, slippery materials. She also made a number of formal gowns for her 5 daughters. She tried many tricks, was not really happy with them. She complained to her friends at the sewing machine dealers. They recommended a roller foot, which she did purchase and use. She found it extremely helpful in keeping materials feeding smoothly, evenly stitched.
My mother inherited the roller foot, found it useful also, but passed it on to me with the old Phaff machine it fit. She didn't think she would have much use for it herself. I have used it a few times, works like a charm on the slipperiest stuff. Gauze, tissue, costume materials flow right along for even stitching.
I have seen roller feet available in the sewing machine stores, so they should be available in other areas. Probably have a universal foot that fits most machines. Price wasn't terrible, might be worth a try for you. Perhaps store would let you give it a try while you were there.