Google is friend, but some of it comes down to common sense as well;
Here are some things I keep on hand for multiple uses and general tips -
Scour Pads - https://www.amazon.com/Scotch-Brite-Heavy-Scouring-Kitchen-Cleaning/dp/B001KYQBX0 Can scratch teflon/nonstick and any non metal surface. Uses are for baked on foods on pyrex/glassware/stainless steel/cast iron.
Regular Brush - https://www.amazon.com/Holikme-Kitchen-Cleaning-Bendable-Scouring/dp/B08P2V5C5Q Good for lightly soiled anything, included non-stick.
Food scraper - https://www.amazon.com/Scraper-Plastic-Multifunctional-Non-Slip-Resistant/dp/B099DTPRSJ Just for removing stuck on bits, and is plastic so feasibly used on any surface.
Barkeepers Friend - https://www.amazon.com/Bar-Keepers-Friend-Powdered-12-Ounces/dp/B000V72992 Specifically for polishing stainless steel/metal back to original finish. Can take care of oxidation or really carbonized stains. 'Kitchen safe' Oxalic Acid (organic/naturally occuring acid), means it's strong, but not completely toxic. (Article)
Do not underestimate the power of a good soak. It can make the work of removing food bits easier. I try to never put food bits into my dishwasher, dishwashers have a particle trap, but doing the work on the frontend is just more logical to me. Get stuck food bits OFF dishes beforehand.
Learn your dishwasher's spray pattern. And how to face the soiled dishes towards the spray for best packing. Handwash lightly soiled/big dishes. Used a bowl to rinse some veggies? Light soap and rinse is all it needs, don't waste the space in the dishwasher with something so lightly soiled.
Cutting board care. Wood has specific steps you should follow included 'sealing'. The quick summary of this is as follows; you use mineral oil on the wooden board, the wood absorbs this oil at surface level, and it 'hardens' the wood. This means water and bacteria does not soak and fester past the oil layer, and cuts from the knife do not do as much damage to the board. If you are not interested in oiling and caring for wooden board, I would not bother.
For this reason I use plastic cutting boards. If you cut raw meat on a cutting board you have to 'sanitize' the board. I do this by using the dishwasher instead of handwashing. Dishwashers water temp is enough to sanitize I believe (150F+). If your cutting board is used for non-meat products, handwash and dry is perfectly fine, and doesn't require special care. For this reason I have a cutting board designated for meat cutting, that I ALWAYS put into the dishwasher after use.
Teflon and non-stick products will eventually lose their surface. Many cooks consider their teflon products as 'short term' products. With how cheap some of this kitchenware gets, that is a fine mindset to use. Use only soak and soft soapy sponge on teflon, as well as using only soft utensils on it, and the finish can last a while still. Also a very high heat can induce wear. So don't use your teflon product to dry-sear at high heat, I've found medium to medium-high heat is as far as I go.
Cast iron is it's own thing you can dig into, but luckily google provides many results for help.