Lighting, Light Fixtures, Ceiling and Exhaust Fans - Connecting to the old wiring

In a previous post, I asked about which junction box to use.

Now I need to ask specifically about wiring a new ceiling light and connecting to the old 2-strand wiring. Are there any special concerns? I know an electrician would tell me to pull out all the old wiring, but that is beyond my skill and would be quite expensive to do. (I don't want to spend $200 to have an electrician rewire for a $30 light fixture.) Is there any special I can do to make this more safe? Something that connects between the old wires and the wiring for the light fixture, which will have a ground wire?

Code does not permit the extending of an ungrounded circuit. Are you sure it is not grounded. Even though there is not bare ground wire it could still be grounded depending on the wiring method.
For example if there is conduit then the conduit could be the gorund.

The wires that connectedo the old fixture were inside flexible metal conduit. The wires/conduit are still intact, but not quite long enough to reach where I need to place the new junction box--about 8 inches too short. I assume this is a common problem in older homes. I wanted to see if there were some sort of instructions online (preferably with photos or drawings) that would tell me how to do this? I have changed out 4 different ceiling fixtures in the house, but in each case there was already a fixture in the center of the ceiling, so it was a simple matter of disconnecting the old/connecting the new. This is my first attempt at replacing a recessed fixture and switching to a ceiling mount fixture

As to the comment about wiring being to code, when I bought the house a question came up on inspection about grounding something to a cold water pipe. An electrician was called in to fix the problem at the seller's cost and the house then passed. No other problems came up on the inspection aside from the need to install GFCI outlets in the kitchen/bath areas.