Well, I don't have a 5DIII yet, but from the manual this appears to be very much the same to set up as on 7D....
On 5DIII, go into the menu and navigate to the Camera Setup 2 tab.
Scroll down to Custom Controls and select it.
This should show an image of the camera button and control layout.
First go to the Shutter Release Button and deselect AF or AF Start from it. Choose one of the options that doesn't include AF start
Then navigate to the button you want to assign AF to on the back of the camera (usually AF On or */SE Lock).
The AF On button, if that's what you choose to use, should be set up and ready to use this way by default.
If instead you choose to assign AF Start to the * (AE Lock) button, don't forget to assign AE Lock to the AF On button.
The Custom Control layout is described in a great deal more detail starting on page 321 of the 5DIII manual.
In other words, it's now at least a two step operation, to unselect AF Start from the Shutter release button and to reassign the function to one of the alternatives (but one of the alternatives - AF On - should be set up by default).
I believe metering start, and IS start for that matter, will follow whatever you set to start AF. However, I notice on my 7Ds (which are similar) that I still get both metering and IS start also occur with the half-press of the shutter release button. That's not a problem in any way, as far as I can tell after using the cameras set up this way for a couple years now.
Geez, 400+ page user manual! That's got to be a new record for a Canon model short of the 1D series with all their customizability.
EDIT: This article in the Canon Digital Learning Center might be helpful, but needs to be updated with new models, lacks any info about the 5DII and doesn't really go into much about the 7D, which seems to be similar to 5DIII (but, again, this is just from reading the 5DIII manual).