How do I install the cable to the hood latch on my 2002 mercury sable

you have to finagle it along the old one and slip it into the attaching holes

Did the old cable break? If it did, then you need a new cable. If you have a new cable that you are installing, then just hook the round barral on the end of the new cable onto the hood latch release lever before you put the retaining nut into the cable. You have to hook it up before you put the retaining nut in because you have to be able to rotate it 90 degrees.