Cutler Hammer panel and whole house Generator
Separating neutral and ground on a Cutler Hammer panel is as simple as installing an accessory ground bar.  They sell those (now under the Eaton brand, but still marketed as CH or BR) and the panel should have holes already drilled and tapped for the mounting screws that are in the kit.  

If for some reason yours does not have mounting holes that line up with screws on standard ground bars for your panel, you can physically mount it some other way that reflects good workmanship (NEC 110.12). 

I am not the biggest fan of screws as a method to make electrical connections, so if the panel's metal chassis figures into grounding anythingv(like metal conduit leaving the panel), I recommend a burly grounding strap from ground bar to panel chassis, separate from the mounting screws.  

Lastly, remove the grounding screw or strap from the neutral bar.  Right now the neutral is grounded to panel chassis, and you no longer want that.  

Occam's Razor: install a subpanel

There's a better and less disruptive way to do all this.   You can fit a proper subpanel next to your main panel.  You then move the circuits you want supported from generator, into that subpanel.  

If the generator is permanently installed and not GFCI, remove its neutral-ground bond and use some ingenious generator interlock hardware made by actual tier 1 panel maufacturers (so you're not paying top dollar for hacked up rubbish like Reliance switches). For instance a Siemens 16-space "subpanel as transfer switch" costs about $130 and is top shelf.  

If you want to use a portable generator that you will be hauling away to other tasks, you will need to switch neutral. The same principle applies, but you put the 3-pole transfer switch immediately next to the subpanel.