These are suggestions to try. Clean the lint, dust, thread pieces from the bobbin area, the feed dogs, and under the needle plate. Oil the machine according to the manual--use only fresh, good quality sewing machine oil.
First, make sure to install a brand new needle and verify that it is installed facing the correct direction. Confirm that the needle you are using is compatible with the thread and fabric of your project. Spend a couple extra dollars for good quality needles. You don't have to buy Schmetz, as there many other good needles on the market. Avoid the generic or cheaper brands. All About Needles
(see the troubleshooting guide especially)
Check that the thread is not too large for the needle's eye. If the thread is shredding and eventually breaking, it could be old or poor quality thread or the needle is shredding the thread. Some needles have a larger groove (scarf) on the back above the eye that protects the thread as it pierces the fabric over and over. Sometimes, coarse fabric will tend to shred the thread because it acts much like sandpaper.
Try a different brand of thread--preferably a good quality brand of thread. Avoid using old or bargain bin thread. Some machines can be very finicky so some experimentation may be needed to determine the brand of thread that works best.
When threading the machine, ALWAYS RAISE the presser foot throughout the process so the thread will seat properly in the tension disk. Confirm with the owner's threading instructions that the thread follows the correct path and does not skip any guides or wraps around something. Also check that the thread spool does not have any nicks or burrs that may be snagging the thread as it unwinds. May seem trivial, but confirm the thread spool is unwinding in the correct direction on the spool pin. Thread is twisted when it is made. If it comes off the spool in the wrong direction, it will reverse the twisting, making it loop, knot, and weaken as the fibers untwist.
When sewing zig-zag, generally the tension needs to be loosened more than straight-stitch, otherwise it can cause the fabric to create a "tunnel" between the zig & zag stitches. If the fabric tunnels, the tension is too tight. The tension is correct when both the upper and bobbin threads meet in the middle of the fabric. It doesn't matter if your tension is set @ 5 or 2 as long as the upper & bobbin threads meet where they should. The upper tension setting is not static. It is meant to be adjusted, probably every time you change needle, thread, or fabric. Always test the tension on a piece of scrap fabric from your project. Duplicate the situation you plan to sew, ie use the same needle, thread, fabric, the number of layers of fabric, stabilizers, etc. on your test. Then when you sew your project, you will know that it is set correctly.
One last thing to check--look for any nicks or burrs in the bobbin area, ie the hook, the needle plate. Frequently, when a needle breaks, it will create a notch or nick where it has hit the hook or plate. That nick will tend to catch thread and cause it to break or stitch improperly. You can wrap your finger in a piece of hosiery or other fine fabric and run your finger around the metal parts to see if it snags anywhere. If it does, sometimes if the nick is small it can be smoothed with a fine emery board or sandpaper. However, if the nick is large, you will most likely need to replace the part or take the machine to a technician.