Usually disabling the Search application will do that, but it won't do anything to give you more room on your homescreen. It'll just disappear and be unused space still.
If you're looking to remove the search bar and replace it with more icons or not have your homescreen look funky (and btw you'll keep your Search app!), just use one of the many popular 3rd party launchers (I think Nova and Apex are popular). They all have the option to configure to hide the search box, and even replace it with a 5th row of icons on the homescreen.