It's a safety thing, but not required to operate. If I were setting it up to run my house, I'd probably ground it to the same ground rod that the house uses.

Grounding Requirements for Portable and Vehicle-mounted Generators

Under the following conditions, OSHA directs (29 CFR 1926.404(f)(3)(i)) that the frame of a portable generator need not be grounded (connected to earth) and that the frame may serve as the ground (in place of the earth):

The generator supplies only equipment mounted on the generator and/or cordand plug-connected equipment through receptacles mounted on the generator, § 1926.404(f)(3)(i)(A), and
The noncurrent-carrying metal parts of equipment (such as the fuel tank, the internal combustion engine, and the generator’s housing) are bonded to the generator frame, and the equipment grounding conductor terminals (of the power receptacles that are a part of [mounted on] the generator) are bonded to the generator frame, § 1926.404(f)(3)(i)(B).

Thus, rather than connect to a grounding electrode system, such as a driven ground rod, the generator’s frame replaces the grounding electrode.

If these conditions do not exist, then a grounding electrode, such as a ground rod, is required.

If the portable generator is providing electric power to a structure by connection via a transfer switch to a structure (home, office, shop, trailer, or similar) it must be connected to a grounding electrode system, such as a driven ground rod. The transfer switch must be approved for the use and installed in accordance with the manufacturer’s installation instructions by a qualified electrician.

Grounding requirements for generators connected via transfer switches are covered by Article 250 of the National Electrical Code (NEC).

The way I hook up my generator, developed over several hurricanes and one winter storm (and a few thunderstorms) is using a very heavy extension cord (50 amp) run to the main breaker box and hooked to a 50 amp double pole breaker. The other end of the heavy cord plugs into the 50amp 220 plug on the generator. I plug this breaker in and shut off the main to prevent feedback out to the main line so as to keep linemen safe. This feeds both 110V busses. I shut off any circuits that draw too much or I plan on not using. I have never used and kind of ground other than the grounding buss in the breaker box.

On the instructions,