The Car Talk Jump Starting instructions are excellent. I would add: After jump starting a battery it should be fully charged. A full charge will require a few hours on a battery charger. It will recharge just by running the engine, but a lead acid battery needs to be recharged as soon as possible to prolong its life.
To me both should be recharged. Jumping takes quite a bit out of the donor battery as well as the receiving battery. Since my diesel days though of 24 volt starting, I just don’t jump cars any more. There’s too much to go wrong.