On the stock launcher, you can't. Download a different launcher (I suggest holo), press home and select holo or other, to use it, then set it up. There will be an option to disable persistent search bar.

 

No problem, I don't like that bar either.

 

On my Rise I don't mind it. On my Nexus 10, with the drag-home-to-search function, its redundant.

 

If you Root your phone, you can use Titanium Backup to freeze or uninstall Google Search.

 

You don't have to have root to do this. Just go to Settings>Apps>All>Google Search>Uninstall updates>OK>Disable. Hope this helps.

 

You can disable it that way, but you can't reuse that space for shortcuts or widgets, and voice recognition won't work any more.

 

If you install a different launcher like "Nova". It will let you remove Google Search and let you utilize the space for widgets/icons. If you don't like Nova you can always try other launchers or delete it. Hope this helps!