I had difficulty when i first started and it turned out to be that the thread I was using (40 wt cotton) was just too soft for the speed I was "driving." If I slowed down the machine to a snail's pace, it worked. But, I didn't want to take months for that project. I switched to a thinner thread that had a bit of poly in it and we sailed! I still have trouble whenever I put in a high end cotton thread. I guess I just need a thread that matches my sewing style.
If the thread is breaking and the tension is ok:
Check the needle - for burrs, and for size and for eye size
Check the spool - try a different one, it may just be a 'bad' batch.
Check that you've rethreaded the machine from top to bottom with the tension discs OPEN. (pressor foot up)
Change to a different type thread
Try changing the speed - if you're pedal to the metal, aim for med - high.
Oh, and make sure the thread isn't getting snagged up. I can't tell you how many times I've broken thread because I folded down my upright spool pin and tucked in the spool for travel, then restarted sewing without replacing the spool on the post! (oops)