With a Macbook air, 2013 in hand, the first thing needs to do is an upgrade of the Mac OS X.

Upgrading to Mac OS X 10.9 Mavericks

Source: macworld.com
Method: Make a liveUSB installer, boot from it(hold “Option” key while in the white booting screen) and do the installation.
Options:
1. Use createinstallmedia – an utility inside Mavericks installer.
2. Use Disk Utility – dd installer boot image to U-disk, then copy installation files.

Suppose we have already downloaded the Mavericks installer(~5.9GB) from Appstore.

Use createinstallmedia

Locate Mavericks installer bundle(a folder) in Applications folder.
Format a >8GB U-disk with “Untitled” as its name through Disk Utility.
Open a terminal, type the following command:

sudo /Applications/Install\ OS\ X\ Mavericks.app/Contents/Resources/createinstallmedia –volume /Volumes/Untitled –applicationpath /Applications/Install\ OS\ X\ Mavericks.app –nointeraction

Note, in this way:

You will not get a Recovery HD partition if your Mac’s drive doesn’t already have one.
Without a Recovery HD partition, “find my mac” will not work!

Steps:

Locate Mavericks installer bundle(a folder) in Applications folder. “Right Click”(Control + Click or tap with two fingers) it, and choose Show Package Contents.
In the folder that appears, open Contents/Shared Support
Double-click “InstallESD.dmg” in Shared Support folder, this will mount the volume, and add an “OS X Install ESD” entry in Finder.
Open a terminal, type the following command:

open /Volumes/OS\ X\ Install\ ESD/BaseSystem.dmg
Launch Disk Utility, select BaseSystem.dmg, and then click the Restore button in the main part of the window.
Plug in an U-disk, drag the desired partition(not the one named EFI) into the destination field on the right.
Click Restore, and click Erase in the poped warning dialog.
Eject the BaseSystem.dmg in Disk Utility (select it and click Eject button in the toolbar)
Open the destination(with label ‘OS X Base System’) partition, open System/Installation folder.
Delete the symbol link named “Packages”, copy “Packages” folder in the mounted OS X Install ESD volume here.