Battery keeps going dead even though it was a new battery

What is your question?

I brought my son his first car a 1997 Lexus ES 300 and one of the things that he did was put a new battery in the car as it was draining sitting at the shop having new tires and a few small things replaced. After a week of so the new battery is dead and when trying to start it there is just a clicking noise. He puts it on a battery charger and after this it will be ok for another week or so but then the battery is dead again? We are about to put it on the road but i'm worried he is going to get stuck with the car because of this issue. Any suggestions on what might be causing this? Please help if you can, Thank you