How to syncing iPad with iTunes? I bought some songs on iTunes with my iPad and want to transfer those songs onto my iTunes on my computer. 

If I sync my iPad with the iTunes account on my computer, it will just erase whatever on the iPad now and import what is in the iTunes library on my computer.

How can I get these newly bought songs in my computer's iTunes account?
You have two main options.

The first is to use iTunes Match (iCloud). Open Settings on your iPad, then tap Music, and turn on iTunes Match; then follow the prompts. The one caveat is it costs $25 per year.

The second option is to sync it to your computer.


Open iTunes, select the Store menu, and choose Authorize Computer.
Follow the prompts, and login with the same Apple ID that you used to purchase the music.
Plug your iPad into your computer using the USB cable that came with your iPad.
When the prompt comes up to Erase or Sync, or Transfer Purchases, select Transfer Purchases.


Side note: Choosing the "Erase and Sync" option will erase any music, apps, or similar purchased content from your device, and replace it with whatever music, apps, etc. you have in your iTunes library. (It is possible to re-download those purchases, so all is not lost in that event). That is obviously undesirable so you must authorize your computer before transferring purchases. 

You may find this Apple article helpful as well.