Your owner's manual comes first
Every manufacturer lists service intervals for its engines. Use those as your baseline. The guidance below is general and meant to help you build good habits.
Run it regularly
A generator that only runs during emergencies is the one most likely to fail during one. Many owners start their generator about once a month and let it run for a short while under a light load. This keeps seals lubricated and moves fresh fuel through the system.
Oil changes
New engines often call for an early first oil change after a short break-in period, then regular changes based on hours of use. Small generator engines hold very little oil, so keeping it clean and full matters.
Fuel care
Use fresh fuel and a stabilizer if it will sit. For long storage, many owners either run the carburetor dry or drain the fuel per the manufacturer's instructions. This one habit prevents a large share of no-start problems.
Seasonal check-up
Before storm season, winter in the mountains, or a camping trip, check the air filter, spark plug, cords, and outlets. Dust in southern New Mexico clogs air filters faster than you might expect.