how can i control my new mac mini using my new macbook air? Thanks

Sceen sharing is built into the OS go to your help in the finder and type in "screen sharing"

To set up screen sharing: (on the mini)

1. Choose Apple menu > System Preferences and click Sharing.
2. Select the Screen Sharing checkbox.
3. To specify who can share your screen, select one of the following:
4. All users: Select this if you want to allow any user with a user account on your computer to share your screen.
5. Only these users: Select this if you want to restrict screen sharing to specific users.Click Add ➕ at the bottom of the Users list and select a user from Users & Groups (accounts you have set up in Accounts preferences), Network Users (users on your network), or your Address Book. Or click New Person and enter a name and password to create a sharing account. Then select that user from the list and click Select.
6. Click Computer Settings and set the following options:

7. Anyone may request permission to control screen: Select this to allow anyone on your network to request to share your screen.

8. VNC viewers may control screen with password: Select this and enter a password that VNC viewer applications can enter in order to control your screen.

9. It’s recommended that you not set a password if you only share this computer’s screen using the built-in screen sharing viewer in Mac OS X.

and yes theye are clients to run on the ipad that can use screen sharing too...i set it up on my wife's ipad, but she's in CA right now....I think it was VNC viewer, but I can't double check

Acutally i realize the app I used on the iPad is "Remoter VNC"