This is something that I see people neglect a lot beyond the odd wash/wipedown, especially with Matte finished frames where the dirt doesn't show, unlike a gloss frame.
While carbon fibre composites are wonderful materials they still need attention like the steel and aluminium frames you may have had previously. Areas of your frame that see a lot of wear (inside of forks/chainstays, drive side of BB, bottom of downtube) or a lot of sweat/rubbing (top/headtubes, outside of chainstays) need attention to make sure that the finish of the frame isn't compromised, exposing the composite materials.
This is especially important with lightweight frames, as they will usually have a lighter, softer finish to achieve that low weight.
The first thing I do when I get a new frame is clean it thoroughly and then apply clear frame stickers to the following spots:
Drive side chainstay - to stop chain wear, and heel rub if necessary
Both sides of the headtube - making sure that cables cannot rub against the frame
Top of the seattube (if it has a seatstay mounted brake) again to stop cable rub
Behind the chainrings on the drive side chainstay, to prevent wear and chipping from a dropped chain (some frames already have a protector for this purpose.)
These can really speed up wear and flaking on a carbon frame. Sweat, dirt, rain and mud can get it and make them grow at a rapid rate. Most common places are the downtube, seatstays and headtube but they can appear in other places.
Small chips can be easily treated when you spot them early. Clean the area thoroughly and then seal it with something such as shellac or even clear nail polish. More than one coat may be needed to seal it completely.
One of the most important things is to recognise which parts of the frame get exposed to the most sweat, dirt, mud etc. My knees have always come in towards the top tube at the top of the pedal stroke, so I need to keep it clean or it will wear quickly and become "polished". I also sweat a lot more than most people so I need to keep an eye on my headtube as well, as the sweat can get into the headset, as well as under the edge of the coat.
Sweat eats away at the finish of your bike quickly, so be sure to clean it (or at least wipe it down) after every long ride. Don't be "that guy" who always has a filthy bike, then wonders why the finish on their high end frame only lasts a year or two.
Baby wipes can be a great way to get your bike clean quick, but I avoid using them too often as some brands can wear away the paint over time. The best thing is to get a good bike wash product and use some elbow grease.
When I give my bike a thorough wash, I degrease the drivetrain first, focusing on the chain and rear derailleur. After this I'll scrub it down and rinse off, avoiding getting water into the bottom bracket and headset as much as possible. Then I dry the bike down thoroughly. Pro mechanics generally air dry bikes after a wash to reduce moisture ingress as much as possible.
Once the bike is washed I'll check that there's no grit or dirt in the brake pads, that the bar tape is clean and intact, and check the bottom bracket and headset are clean (no obvious dirt, grease etc). I'll then lube the drivetrain lightly and give the frame (not the drivetrain) a very light wipe over with a spray on cleaner like Mr Sheen, silicon grease, WD-40 or even a very light chain lube to give it a barrier and shine the bike up nicely.
With the wheels, I will give the rims a clean with methylated spirits to make sure that the braking surface is clean and the pads grip nicely without squealing. I'll also check the cassette for any trapped gunk and if necessary remove and clean with degreaser. Every 3rd or 4th wash I'll put a tiny drop of chain lube on the nipple of each spoke to make sure that it won't strip when it comes time to true or tension.
Good things to have when cleaning your bike:
2 buckets of water - one for detergent, one for rinsing
Degreaser - I usually use methylated spirits or a bike specific degreaser
A soft scrubbing brush with long bristles
A 1" paintbrush for degreasing the drivetrain
Baby wipes for wiping off excess mud/dirt from the drivetrain
Soft cleaning cloths
Old but clean towels/rags for drying
Rag for wiping off excess chain lube
Spray on cleaner/very light lube