First off, have you considered that the fridge manufacturer might be silly and lazy in not making their appliance GFCI-compatible? Although the shock risk from a properly grounded fridge is low, I'd consider returning the fridge for one that doesn't have this caveat in the manual.
That aside, this is not much different from any other breaker changeout.
Before doing this, I'd ask the power company to kill the power to your house while you work on it (modern smart meters can be disconnected remotely, even) -- that way, you don't have to worry about working around live parts at all. I'm mildly paranoid about live parts though; if you're not that way, you can simply turn the main breaker off and avoid the main breaker supply lugs while you're working, as they'll still be quite hot.
Also, the new code (2017) requires the use of torque tools to torque terminal screws to specification (this avoids loose or overtightened connections, both of which can fail over time) -- there should be a torque spec on the panel's labeling, and you can pick up a cheap torque screwdriver for oh, $50 or so at one of the big box stores.
Once everything's dead and you can safely pull the deadfront, remove the GFCI breaker from the busbar, tag the hot and neutral wires, and disconnect the hot and neutral wires for the circuit from it -- you'll have to unscrew the terminals to do this. You can then remove the neutral pigtail on the breaker from the neutral bar and land the tagged neutral in its place. Take the new regular breaker and install it in the open slot left behind by the GFCI breaker, then attach the tagged hot to the new breaker and plug it onto the busbar (again, you need to torque the terminal screw to spec here). Put the deadfront back on, and have the power company turn the power back on.
BTW: a non-GFCI breaker here is Code-legal as 210.8 point 6 only requires GFCI protection for kitchen countertop receptacles. A dedicated fridge circuit's receptacle serves no countertops, so it does not require GFCI protection.