What is the best way to clean small pieces of twigs and dirt from the gears?

Soap and water.

After 20,000+ miles

You only clean them every 20,000 miles.
That’s amazing!

Barry

What kind of riding do you do and how dirty is everything else? For a bike ridden off road in mud or through lots of moist loose dirt, a pressure washer might be appropriate for the gears and much of the rest of the bike.

For road bikes, I use moist towelettes that come in bottles similar to clorox wipes and after they've been used on the frame, I roll them up or twist them and then see-saw them between the cassettes.

Though, I'm not going for spotless like GlennR . I'd have to make sure I hide my bike in shame if I knew he was around. However I admire those that do take the time to clean that well.

Yes it is.

Seriously I clean the bike every week which is around 150 miles.

I have a CX bike that is my winter and foul weather bike. I ride it about 1000 miles a year in rain, snow and wit hall that road debris you have in the winter. At least once during the winter, I bring it inside to clean the drivetrain but the bike is relatively filthy. The drivetrain is Sram Rival CX1 so I replace the chain every Spring. The cassette and chainring are still OK after 5 seasons.

Road bike should be clean, but a clean MTB or CX bike means it's not being ridden

twigs & dirt? brushes made for the purpose like this one

Muc Off Claw Brush

How clean the bike gets depends on whether I'm going to take a picture for the ever-critical Internet, or just to get crud out of the way so it works.

pick tools & rags.

If the mechanicals operate as expected during the ride, then the previous detailing was good enough. If the non impeding grime is an annoyance, then more picking & rags with some appropriate cleaners can help with that.

I like to go purely mechanical for the first pass if it's really heavy build-up; nylon bristle brushes are good for general surfaces, I also like to use an old shoelace to "floss" the cassette cogs. Bamboo skewers or chopsticks can be used to dig in to tight spots or scrape areas that might need more than a brush, but might be damaged by something like a screwdriver.

If you MTB in wet, muddy conditions, or deal with a lot of used, semi-neglected bikes, you can go through a lot of cleaning supplies. These are some more economical options, you've probably got some around your house already.

I take it in the shower with me. I try to shower daily.

Stiff brush. I get 'em from the dollar store so I don't feel bad about throwing them away when they get gunky or torn up. A dollar store toilet brush works fine for gunky drivetrains, hubs, spokes, etc. Sometimes they carry smaller stiff bristled plastic utility brushes so I'll buy a few when they get 'em.

Cheap shoelaces to clean between the cogs on freewheels/cassettes. I moisten the laces slightly with a bit of goo remover, WD40, whatever's handy. Works like dental floss. Flat cotton laces get snagged and torn up after a few uses but are cheap so I discard them after a few uses. Braided laces last longer and don't snag as easily on the teeth, but need to be cleaned occasionally.

I also use the see saw method. Usually with a paper towel or shop towel. Not sparkling clean like the above pic but nice and slick. Often noticeably quieter when riding after a good cleaning.

Chain cleaner is available in market. Spray it as per requirement. Then apply chain lubricant which is available online also.

Once u apply chain lubricant it lasts for 20–30 days. But when u wash bike with pressure u need to pit chain lube after it gets dry

I've never gotten my gears that clean. Maybe make a video and post it?

do you guys "floss" your cassettes with old shoe strings or strips of cloth?

For the big chunks I use a Park GSC-1. The hard end fits between the cogs and is strong enough to pull chunks out. If I really want to get it clean I'll disassemble the cassette and/or "floss" the cassette.
Finish Line Gear Floss

I use an old school park cyclone chain cleaner (I call it old school because its 20 years old lol.) on the chain which gets some degreaser on the cogs. I then hit the cogs with some foaming degreaser for max coverage and let it soak. I then fold a paper shop towel (a bit tougher than a standard paper towel) to make it thin and go between the gears. When it starts to shred a bit I refold or switch to a new section of towel. Not as clean as the above bike but it usually is pretty good. I always do the chain and derailleur cogs at the same time. I love a quiet drive train when pedaling. Mine needs a good cleaning as we speak !!

This might help... I dismantle the bike every winter and use a ultrasonic cleaner, with just hot water and Dawn,to clean the parts. But I do clean the cassette with Simple Green and a tooth brush once a week, or round 150 miles, so it stays clean.