Here are some troubleshooting tips...
Machine isn't sewing at allIf your machine isn't sewing (but is plugged in and switched on!), it's likely to be because either the needle has come unthreaded, or the bobbin thread isn't pulled through to the top of the stitch plate.
Needle unthreaded: Sometimes the needle will come unthreaded when you start sewing if there wasn't enough loose thread pulled through to begin with. Re-thread the needle, and pull about 10cm of thread out towards the back of the machine before lowering the presser foot onto the fabric and starting the seam again.
Bobbin thread: Check whether the bobbin thread is coming up through the stitch plate, and that it runs freely when you draw it gently backwards. If not, hold the end of the top thread (with needle threaded) in your left hand, and turn the balance wheel towards you until the needle moves down into the stitchplate and up again. It should bring a loop of bobbin thread with it, which you can carefully hook with your scissors or a knitting needle to catch the end. If this doesn't work first time, continue holding the end of the top thread while you turn the balance wheel forward again.
Puckered fabricThis is usually down to either the top thread or bottom thread having the wrong tension. Sometimes if you're using a zig-zag stitch it's because the fabric is too thin, but you should still be able to correct this by adjusting your tension. If the fabric is thin, zig-zagging the raw edge will nearly always cause it to roll - this isn't a problem, as you're probably zig-zagging to prevent fraying, but if you need an accurate seam allowance it's best to sew the straight-stitch seam line before you zig-zag the raw edge.
Tension problemsWhen your machine is sewing properly, you should only be able to see the top thread on the top surface of the fabric, and only the bottom thread on the bottom surface of the fabric. (This is easier to check if you're using different colours of thread on the spool and the bobbin, and both contrast with your fabric).There should be no small loops of either thread pulled through to the opposite side. If you can see these loops, read on....
Bottom thread shows on top of the fabric
Either your top tension is too tight or your bottom tension too loose. Top tension is easier to adjust, so start with that - move the dial to a lower number and do a couple of inches of test stitching. If the stitching has improved, you can make further slight adjustments to perfect it.
If you top tension dial was already on a very low number, you may need to increase the bottom tension instead/as well (note that some machines do not have the facility to adjust bottom tension). To increase bottom tension, remove the bobbin carrier; on the side of it, you will see a small screw head. Using a small screwdriver which fits, turn the screw head clockwise a quarter turn. Replace the bobbin and carrier in the machine, and do some test stitching. If the stitching has improved, you can make further slight adjustments to perfect it.
Top thread shows on bottom of fabric
Either your top tension is too loose or your bottom tension too tight. Adjust the top tension by moving the tension dial to a higher number, to increase tension, and do some test stitching. If the stitching has improved, you can make further slight adjustments to perfect it.
To loosen bottom tension, remove the bobbin carrier as above, and turn the screw head a quarter turn anti-clockwise. Replace the bobbin and carrier in the machine, and do some test stitching. If the stitching has improved, you can make further slight adjustments to perfect it.
Sewing is very noisy/thumping
Your needle may be blunt and need replacing. Check the sewing machine manual to find out how to do this.
There may be excessive lint or pieces of thread caught in the mechanism underneath the stitch plate. You can remove the bobbin carrier and the front part of the bobbin locator to clean out accumulated fluff and dust - doing this always makes your machine run better! Check your manual to find out how to do this (and put the pieces back together) for your particular machine.