Q: My mom and I use the same iTunes account. I have my own list of contacts and she has her own. How can I prevent my contacts from going into her contacts and vice versa?
A: This depends largely on whether you are syncing your contacts via iTunes or using iCloud.
If you are syncing your contacts from a local address book using iTunes on a family computer, the only way to avoid sharing a single contact list is to either disable contact syncing on one (or both) of your devices.
You could still maintain your contacts locally on your device, but they would no longer be synced with your computer and changes would therefore not be transferred over to the other device. The setting for this can be found in the Info screen for your iPhone, iPod touch or iPad sync settings in iTunes.
Alternatively, if you setup a second iTunes library under a separate Windows or Mac user profile, you can sync your contacts separately with the address book for that particular user profile, effectively maintain each of your own separate address books.
If you are using iCloud to synchronize your contacts with your iOS device wirelessly, then the solution is actually somewhat easier; simply setup a different iCloud account on one of the two devices.
While iOS will setup both iCloud and iTunes to use the same Apple ID when you first configure your device, these do not have to be the same; you can simply go into your iCloud settings, delete the current iCloud account from your device, and then setup a new one from scratch. See Moving from a shared iCloud to individual accounts for more information.
Even after doing this you will still be sharing the same iTunes account for things like iTunes Store purchases, unless you also change your iTunes Store account. Similarly, you can choose to use the same or different Apple IDs for other services such as iMessage, FaceTime and Game Center.