Everyone wants their car to look as good as it can, but it can't be maintained simply by washing it once every two weeks in an automated car wash. For your car to look its best, you need to take care of it, and that's where polishing and detailing the car comes in.
What's polishing and detailing?
Polishing is a simple process. You use a very fine abrasive material and by using mechanical action (a drill, your hand, etc.) you make large uneven portions height wise in your paint smaller and flatter. Large is an exaggeration, more or less. You can't see it with the naked eye, but your paint is formed out of microscopic ridges, which can vary a lot in height which make the paint look dull. The light doesn't reflect properly of those ridges and gets "absorbed", and by making those ridges smaller and flatter, you are essentially creating a sort of a mirror. This process can be further improved by waxing, adding ceramic coats and other techniques.
Can anybody polish their car?
Technically yeah, everyone can, but if you don't know what you're doing you can damage your paint pretty badly. It isn't that complicated, and for someone which has a bit of a knack for tinkering and working with their hands it shouldn't be that hard. The best tip I can give is to try and polish a very small area of your car, somewhere which isn't very visible.
Can you just start polishing from the get-go?
No. The car needs to be very clean before polishing can start. Not even a simple wash is enough. By not cleaning your car properly, you leave small debris on the paint. If you start polishing your car and catch those debris while polishing, all you do is drag that small debris around the paint, removing small scratches and creating them right back, simply because that debris acts like sandpaper.
So, how do you clean your car properly?
Well, first and foremost give it a good soak in water to clear all the large particles of dirt, dust, etc. Do it from the top of the car to the bottom of the car. The gravity will make the water drip downward, if you start from the bottom lip and go to the roof, all you do is move the dirt from the bottom of the car to the middle of the car. After that, get two buckets, one with water with some detergent (check and see that whatever detergent you are using works fine on paints), and one with plain water. Get a microfiber cloth, not just some old t-shirt or rag, because they are finer and better at cleaning than an old rag, and start washing the car, again, from top to bottom. Wash it for a bit, rinse the cloth in the plain water bucket, and fill your cloth again with soapy water. Do this for the whole car. After the car sat there for a bit all soaped up, rinse the soap.
Can I start polishing now?
If you want to do a proper job, then no. Believe it or not there are still small dirt particles and very small stones stuck to the paint. To get rid of those, you need to get a clay bar, or a clay glove. By dragging them slowly across the paint in linear motions, you will slowly but surely catch all the small debris and impurities.
After I clay bar the car, can I start polishing?
Yeah, no reason not to do it, other than the fact that the paint could also be looking decent by now. If you see some major scratches, swirls, or others then polishing is probably needed. Also, a very fine polish works very well, because the clay bar leaves some trails, blotches, and other small defects along the paint, by polishing it finely you get rid of those too. Polishing is a bit more complicated to explain, and I recommend watching a video of someone doing it in whatever fashion you want to do it, but the gist of it is as follow: get some polishing paste, use some on whatever material you are polishing with (a felt disc as an example) and start polishing. Spread the paste around by swirling and start polishing by applying a small amount of pressure on the drill/hand/etc.
Can I just finish with a polish?
You could, but it's pretty unfinished to some people. Usually after polishing you wax your car with a car wax, with a technique similar to what you do when you clay bar the car. This coats the car in a wax, obviously, but most importantly protects the paint further. Debris and other nasty stuff have to get through that wax first, before it gets to the paint's clear coat or the paint itself, as such, the paint is protected. Another thing you can do is to apply a ceramic coating, which acts similar to a wax but lasts longer. Some ceramic coatings are better than others, and some are more complicated to apply and more expensive than others, so leave those to professionals.