Check to be sure you are using needles and thread that are compatible with the fabric. Generally, finer threads will work better on fine fabrics along with a smaller needle. Be sure to change needles frequently as dull, bent, or nicked needles will cause very frustrating issues. All About Needles
Remove the thread completely from the machine. RAISE the presser foot and rethread from the beginning, making sure the thread path is correct.
Some machines have a presser foot pressure adjustment (consult the owner's manual). Adjusting the pressure that the presser foot applies to the fabric & feed dogs is helpful when sewing especially fine or heavy fabric. Also, when sewing fine fabrics, loosening the tension could be beneficial.
Changing presser feet may also help, ie try using a straight stitch foot vs a presser foot for zig-zag stitching.
Something else you can try is finding a presser foot with a teflon finish or a roller foot that will glide or roll with the fabric through the machine. Even if you can't find a brand name presser foot for your particular machine, an adapter shank can probably be found that would allow you to use snap-on feet of all different designs and uses. Provides a lot of choices for presser feet for less than purchasing a brand-name presser foot. There are snap-on kits available on eBay and other auction sites.
Some machines also can take a straight-stitch needle plate--usually an additional accessory that can be purchased. The hole where the needle penetrates the needle plate to access the bobbin thread is actually a small round hole. With a zig-zag needle plate, the hole the needle penetrates is a wide rectangular hole that can allow fine fabrics to be pulled down through the hole. Zig-zag capable machines usually have a zig-zag needle plate as standard.