You need to transfer your iTunes library from your MBP to your MacBook Air. Copy the iTunes named folder in your Music folder on your MBP and with iTunes quit on the Air, place the iTunes folder in your Music folder. You will also need to authorize your Air with your iTunes account with iTunes.
Before syncing contacts with the Address Book and calendar events with iCal on the Air, enter one contact in the Address Book and one calendar event in iCal on the Air. This will provide a merge prompt with the first sync for this data, which you want to select.
If you use iPhoto for importing photos from a digital camera and for photo storage and management on your MBP, you can transfer your iPhoto library from your MBP to your Air. On your MBP, go to Home > Pictures. Copy the iPhoto Library and transfer it to your Air.