Agree with checking tension, putting new needle in & make sure the presser foot is down before you start sewing (!) Also check that you are using good thread as not all thread is created equal.

Also drag out the manual and check you are threading the machine properly. If you miss one of the little hooks it will affect the tension. Likewise, check the bobbin too. Start sewing half a centimeter from the edge and lower the needle manually for the first stitch.

If the fabric is very thin you could add a layer of baking paper or tearaway stabilizer to help with sewing.