The simplest way is to select the object you want to be invisible in the render, then right click and select object properties..

If By Layer is highlighted under Rendering Control, change it to By Object by clicking on it.

You can then uncheck Renderable to make it invisible to render, casting shadows etc, or individually uncheck visible to camera, if you want it to still cast shadows, visible in reflections etc.
You can also make an object appear see though by adjusting the visibility spinner from 0,0 ( invisible ) to 1.0 solid.
Some of these settings will not work correctly depending on the renderer you are using.
Another method is to apply a material to the object, set things like reflections and glossiness to zero, and make it 100% transparent., but I think the first method is probably what you are looking for.
Hope that helps.
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