It's not a vintage machine.
Threading is very similar on all of these older machines, so shouldn't be difficult to figure out. The arrows tell you the thread path to follow. The only thing that might require some fiddling is figuring out that first tension guide (the plastic one on top), but it looks as if you figured that out. Here is a link to a Youtube video that shows the typical thread path:
http://www.youtube.com/watch?v=-DexrUyBQpA
Are you making sure that the presser foot is UP when you thread the machine? That is necessary in order to seat the threads correctly in the upper tension discs.
One thing I see is that the type of thread spool you are using should really be placed vertically on the spool pin, not horizontally. I don't have a machine with that type of holder, so maybe someone else can comment on this. I do know that American type spools should be upright; crosswound spools (mostly from European makers) are the ones that should be mounted horizontally like the one in your picture. The red thread does not look like a crosswound spool to me.
You cannot assume that the needle in the machine is the correct one for the machine or that it has been inserted properly. I agree with re-seating the needle, and would also replace the needle if you have one handy.
I cannot really tell from the picture, but it looks as if the upper tension knob is not at a realistic setting. Typically you want to start with it at 5 or so.
Have you tested the bobbin tension? Here is a link to a tutorial on tensions:
http://www.threadsmagazine.com/item/...nsion/page/all
If, after doing all this, the machine still does not bring the bobbin thread to the surface, chances are that the machine is out of time. This can happen when there is a bad thread jam, especially on less expensive machines like this (although it can happen on expensive machines too!). That becomes very technical, as it has to do with the timing interaction between the needle and the bobbin, and usually you take it to a technician for that fix.
If I had to start with just one thing, it would be making sure that the correct needle is in the machine and that it has been inserted correctly.