New sewing machine..........

only a suggestion, try tightening the tension on the spool underneath, sometimes it comes off the spool to fast causing a surplus of thread which can tangle, if this makes any sense.

I would say definitely a tension problem, just trial and error really.

Is the needle sharp ? A blunt needle develops a 'fish-hook' on the point which can snag on the thread.
Make sure when you have fiddled with the tension that you have it balanced. With both top and bottom tensions the thread should be able to be pulled out with just a small amount of 'pull'. ie not too loose and not too tight (test top tension with presser foot up).

Is the bobbin in correctly? The two threads should ideally loop together between the layers of fabric. It may be easier to see what is going on if you use two different coloured threads on a plain fabric. I would use a fabric which is not slippery or very thin for my testing.
Is there a fault and remedy page in the instruction booklet?

The needle should be fine - the machine is brand new.

There is no facility for tightening the bobbin tension, only the upper thread tension.

I'll keep fiddling!

I don't know whether all machines are similar, but on my Frister and Rossman there is a screw on the bobbin case for adjusting the tension.
Have you threaded the top in the correct order? The tension will be up the creek if that is the wrong. When it had been a while since I had used mine I really had to think hard!
I hope you sort it out.

There used to be a little screw on the bobbin casing which altered the tension

Sorry shysal I didn't mean to copy your advice, I am very slow at typing

What make is it Mishap? I have never known a machine which cannot have the spool case tension altered.

If the machine is brand new I would be asking the supplier to rectify the problem and he needle SHOULD be sharp but is it !?

Is the bobbin in the right way round? It may be as simple as that. You should be able to hold the thread and let the bobbin & case dangle - slowly or not at all. The bobbin also needs to be inserted then the thread caught back through the bobbin case.
failing that, is the top thread, threaded up properly? Sometimes problems underneath are actually the fault of the top thread. I tend not to play with the tension...

Is this the first time you have used it? I had to take back a new machine recently. Technically it looked ok, just would not sew and had a similar problem. X