I can almost guarantee you're trying to push or pull the fabric under the presser foot if you're breaking needles. Quit it. You can do some serious damage to yourself or the machine or both. Practice guiding the fabric and letting the feed dogs do the work of transporting the fabric. I have beginners sew on paper first -- paper is easy to handle, you learn to guide the machine, and it tears or buckles if you're pushing or pulling.
Unthread the machine and practice sewing straight lines and curves on plain paper. Watch the edge of the paper/fabric on the guide marks to the right of the presser foot -- don't watch the needle -- you'll be less accurate and you'll get seasick. It knows what it's doing -- going up and down -- you need to learn how to guide the paper or fabric with the correct seam allowance. It'll feel all wrong at first -- persist -- you're not wasting anything except some junk mail or blow in subscription cards out of magazines. When you're happy, let's thread up the machine and sew.
Put in a new needle, right way around. Check the manual. If the bobbin case is towards your belly, the flat of the needle shank goes toward the back. If the needle is wrong way around or the needle isn't fully up in the needle clamp and firmly clamped, you'll break needles.
Front and backs of needles: http://www.picturetrail.com/sfx/album/view/17206792 If you get the needle in backwards, the stitch won't form or will do so only infrequently.
Let's start at the beginning: Take all the thread out of/off of the machine. If you've been playing with the tension dial, reset it to 4.
Raise the presser foot. Use the handwheel (or a button or foot pedal on some machines) to raise the needle and the thread uptake lever to the highest position. Thread the top of the machine, following the instructions in the manual. Raising the presser foot allows the thread to enter the upper thread tension. Pull a tail of thread through the needle about 4-6" long.
Thread the bobbin and bobbin case following the instructions in the manual. Leave a couple of inches of thread sticking out of the bobbin case.
Hold on to the needle thread tail and use the handwheel (or foot pedal or button on some machines) to lower the needle into the bobbin case area, then bring up the needle (so you're making one full stitch cycle).
Pull the end of the needle thread and the bobbin thread will rise through the hole in the needle plate. Pull out some extra bobbin thread and place both thread tails (bobbin and top thread) under and behind the presser foot. You are now ready to sew.
Here's how you're going to sew each and every seam from now on -- this will save you lots of frustration.
1) Raise the needle and thread uptake lever to the highest position.
2) Put the fabric under the presser foot.
3) Using the handwheel (or button or foot pedal on some machines) drop the needle into the start of the seam.
4) Lower the presser foot.
5) Hold the ends of the bobbin and needle threads behind the presser foot for a couple of stitches.
6) Drop the thread ends and sew normally.