It's not like a manual transmission in a car where you normally progress though the gears.

Hopefully you aren't starting off in the big chainring from a dead stop. You're better off starting off in the small chainring and somewhere in the middle of the cassette in the back.

When you start spinning too fast, you either shift to a smaller gear on the cassette or up to the big chainring or both. You should only be in the biggest and smallest gears on the cassette at the extremes such as climbing a steep hill or spinning down the other side of that hill.

When slowing and in the big chainring, shift to easier gears on the back first and to the small chainring in front just before stopping. You can even shift front and back at the same time if you spin the pedals easily.

What you want to avoid is cross-chaining. You don't want to be in big-big or small-small or even a gear or two next to it. It tends to wear out the chain faster. Of course a bike set up properly can operate correctly in those gears, but it's just unnecessarily hard on the chain and gears.