I bought my mac book pro from an owner selling. I created my apple ID but whenever I try to download updates it brings up previous owner's apple ID and asks for password. How do I delete existing apple ID and use mine.

Yes, he purchased Mountain Lion on his Apple ID. It is licensed to him. What he should have done was erase the HDD and install the system that the Mac shipped with. Erase and re-install either from Recovery Partitionor the disks the Mac originally shipped with. Then, purchase ML with your own Apple ID and install.

You need to buy your own copy of ML with your own Apple ID. Then try reinstalling it over top of your current system.