Ill mention a few things here, especially having worked as a detailer for about two years and training people you quickly notice the common mistakes people make when washing cars.
1. NEVER do anything by hand in a circular motion, if you were to have any sort of dirt on your mit or wax or clay bar you will inflict circular scratch marks on your paint which are infinitely harder to remove than straight scratches. Your hand does not move circularly 1800 times a minute like a rotary polisher therefore use straight lines...
2. Polish and wax are NOT the same thing, polish is to cure imperfections in the paint while wax is to protect the paint. Polishing often or cut polishing the car to much will degrade your paint, so regular waxing can extend the time between polishes and therefore make your paint last that much longer.
3. Paint protection kits (often the dealer will try to convince you to buy this along with rust and undercoat and all that crap) is just a different wax compound, it is nothing special and it will wear off after 6 or so months. It does last longer than waxing and it cures really well onto the paint but you do still need to maintain this type of coating.
4. Drying your car correctly after washing is the most key stage, use a proper Shammy or microfiber (never use the glass microfibers as those are meant for picking up lots of dust not water). There are even products you can buy that wax as you dry, and while they are okay, they do not replace regular proper wax applications. But they can make it easier to dry the car and keep it looking good for longer.
5. Dry your door jams and creases and crevices well before waxing, wet wax can be bad. Having an air compressor makes this way easier but I know not everyone has access to those.
Im sure there are mannnnnny more things, but these are just a few key things I figure I would mention that I didn't see above.