How do you get rid of the smell from the pipes in the basement when someone either takes a shower or uses the restroom?

Sounds like your getting sewer gas from somewhere. Try putting some water in the floor drains in the basement. If that's not it look for an opening in a drain pipe. If you have a laundry tub in the basement be sure there is water in the trap. Also make sure the vent stack on the roof is not plugged up. Good luck.

Also make sure the smell isn't coming from the base of the toilet. It would indicate a bad wax ring. You can test it by putting wet toilet paper around the base. If the smell goes away, the ring is most likely bad.

As Chuck said, Check the water level in the floor drain trap. If it's empty then fill it with cooking oil. Give the other traps then sniff test, Good luck, Tom