How to resync my iPhone to a different Mac laptop?

I recently purchased a used Mac from a friend and it has her iTunes still up. I hooked up my iPhone to the laptop to sync my phone to iTunes. However, the two didn't sync up. I want to clear out her old music with the music from my iPhone. Is this possible? And could you instruct me on the steps to syncing my phone to the Mac/iTunes?

To "clear out" files, drag them to the trash, and empty the trash. You can't "bump" her music to the trash by using your music as a battering ram.

You are not using "a Mac". You are using an OS. My answer is for OS 10.8.4.
- Open System Preferences > Users & Groups.
- Click the padlock icon and type the account password.
- Click the + sign to create a new user account for yourself.
- Be sure it is "Administrator" type.
- Quit System Preferences, and log out or restart. (If you get a message about "Automatic login", agree to turn it off.)

As for how to sync, here it is:
http://support.apple.com/.../kb/HT1296

Bear in mind that Apple has always expected that you use the computer to GET songs, and then sync all that to the empty phone. If you want to do it all backwards (use the phone to get songs), try any of these options:

http://www.macroplant.com/iexplorer/ (iExplore, free)
http://support.apple.com/.../kb/PH3267 (iPhoto for iOS -- only for copying photos)
https://www.icloud.com/...cloud.com/ (requires iOS5 for the iPhone/iPod/iPad and OS 10.7.2 or later or Windows Vista with Service Pack 2 or Windows 7)
http://www.dropbox.com/...opbox.com/ (Web storage; free basic limit is 2 GB)
http://itunes.apple.com/...33044?mt=8 (Phone Drive, US$0.99)
http://magnetismstudios.com/FileMagnet (FileMagnet US$4.99)
http://itunes.apple.com/...o%3D6&mt=8 (AirShare, US$9.99, App Store download)

Three more at the "Sources" below.