Connect your iPad 2 to a PC running iTunes and perform a Sync a Backup.
When that si done, disconnect your iPAd 2 and connect your iPad Mini. Perform a restore from Backup on the Mini.
If you synced it many times, you have to have a backup. It's just a question of how old that backup is now. When did you last sync?
First of all launch iTunes on your computer and go to Edit>Preferences>Devices. Do you see any backups for you iPad in that window? If so, how new is the newest backup? That will be the backup that you will want to use. But remember that if you use that backup and it is one month old, you can only restore from that date back in time. Anything that you did on the iPad in the past month will not be in that backup.
Turn on the new iPad Minin and start activating OTA via WiFi. You will get to a certain point in the process where you will be given the choice to Set up as new, Restore from iCloud - or Restore from iTunes. You will want to select Restore from iTunes.
That is the short and sweet version. There are step by step instructions in this article. This applies to the mini as well as the iPad 4 or the iPad 3 for that matter.