If you are working with a slippery fabric, cover your cutting surface with flannel (or flip over a flannel backed tablecloth) to control slippage.
Be sure to use a new, sharp needle that is the correct size for the weight of the fabric you are using. Sometimes light-weight fabrics will pull down into the opening on the needle-plate, so for more support and to minimize this problem, switch to a straight-stitch plate (it has a single, small hole instead of a slot).
Before you do any stitching on your cut out pieces, sew several test seams to determine how to set up your machine to best handle the fabric you are using. Shorter stitch lengths typically work best. If you have trouble with puckering, adjust the tension so that it is a bit looser. If you can't solve the puckering problem, use tissue or another type of light stabilizer beneath the fabric and hold the fabric tight while you are sewing. Remove the tissue/stabilizer carefully after stitching. A special roller foot can also help feed the fabric evenly into the machine.
To minimize show-through, use small (less than 1/4 inch) seams. Sew some test seams and see what look you prefer. The best types of seams to use on transparent fabrics are: French, mock French, flat fell, overcast/serged, hairline, and machine-rolled seams. French and flat fell seams do not work on curved seams such as armholes and necklines so use a mock French or one of the other suggested seams in those areas.
Before hemming your garment, let it hang for at least 24 hours to let the fabric completely relax. If the garment has a straight hem, you can use either a very narrow hem or a wide hem. Wide double-folded hems look wonderful on skirts and the extra weight keeps the hem down and straight. If the bottom edge is rounded or flared, use a narrow hem or a full lining. The reason for this is that the easing that is needed on a wide circular hem will show through to the right side and look odd.
For more detailed information on sewing sheer fabric, refer to the following books:
Good luck and Happy Sewing!