I have a chandelier with eight arms that has 5 bulbs per arm and two wires coming from each bulb. Not sure how to connect the wires. If one wire is "A" and the other is "B", do I wire all five "A's" together? Or do I connect the wire "A" to "B" of the second light.

The first way you describe is parallel wiring. The second is series.

Pretty much all AC wiring is done in parallel.

I must say, if you have to ask this you should reconsider re-wiring a 40 light chandelier. This is no small task.