Short answer: brush the grates every time you cook, do a proper clean about once a month during the season, and give the whole grill a deep clean before you put it away for the winter. Here is what each of those looks like, and how long they take.
After every use: two minutes
The easiest time to clean a grate is while it is still hot. Right after you take the food off, turn the grill up to its highest setting (about 500 °F / 260 °C), then brush the bars while they are hot. Burnt-on food comes off in a few passes; the same job on a cold grate the next morning takes longer. Close the lid, turn off the gas, and you are done.
Doing this every time keeps burnt-on food from building up on the bars.
Once a month: twenty minutes
Even if you brush after every cook, grease and ash collect inside the grill. Once a month, lift the grates out and wash them in hot soapy water, scrape the inside of the lid and the bottom of the firebox, empty the grease tray, and check that the burner ports are clear. Let everything dry before you put it back. If you cook several times a week, do this twice a month.
Before storage and at the start of the season: an hour
Before the grill sits idle for the winter, do the monthly clean plus the parts you normally skip: burners out and brushed, heat shields cleaned, the exterior wiped down, and a cover on it. Moisture trapped under old grease is what causes rust over a Canadian winter. In spring, repeat the check before the first cook and look for spider webs in the burner tubes; they are a common cause of uneven flames.
Signs you have waited too long
Food sticking to the grate, more flare-ups than usual, a sooty smell, or smoke when you first light it are all the grill telling you it is overdue. They add up to worse food and a shorter life for the grill.
What you clean with matters as much as how often
Most grill brushes are wire-bristle brushes, and their bristles break off, stick to the grates, and end up in food; it is a documented cause of emergency-room visits every summer. A loose bristle is nearly impossible to spot on a grate and a brush can shed one at any age, so we recommend not cleaning with one at all. A brush with no wire bristles removes the problem: the Boyer Brush cleans the top and sides of each bar with formed stainless-steel springs, so there are no wire bristles to shed, and it works best on a hot grill, which fits the after-every-cook routine above.