This question has been asked and answered many times in the forum. However, as I just started doing mine (twice yearly) I will tell you how / what I am using. Making a car shine is like painting. The MOST important part is the prep. Even if you use a $250/bottle of wax, you are wasting your time and will get crap results unless the surface is properly prepared. Everything I use on my care comes from Griot's garage, but there are many great product lines out there. To do this properly will take a significant investment, but your car IS a significant investment and so should it's protection be. I will list my products at the end.
PREP:
Do this in your garage, under a tent roof, or at least at a time of day when the sun isn't beating down on the surface. Whether you use a machine or not, this will take the better part of a day to complete, but your car will look better than it did in the showroom when you finish.
1) loosen and remove any surface dirt, sand, etc with a hose. Spray the car thoroughly and do NOT use a pressure washer.
2) while the car is wet, apply car wash with a microfiber mit / cloth. do NOT use heavy pressure or a wash that contains a wax, sealant, or any other additives - just a good quality car wash solution.
3) after each major section, rinse and wring out your mit / towel to remove dirt before using it on the next section.
3) thoroughly dry the car with a clean microfiber towel or chamois, rinsing it between sections same as the wash cloth.
4) buy 2-3 clay bars and watch a video on you tube to learn how to use them properly.
5) clay the car with a detailing spray (meguiars, etc) - NOT water. If you drop the clay on the floor or ground, toss it! It has been ruined.
Now the surface has been thoroughly cleaned, loose particles, road grime, and contaminants have been removed. The surface should feel extremely smooth. On to the second step.
POLISH:
I highly recommend a random orbital buffer. do NOT use the $30 machines at the parts shop. They are worthless, cause scratches, and damage the surface. Use a 'random orbital' machine or do this by hamd with the appropriate applicator.
1) Using a polish (not wax), apply it to one medium section at a time, then remove it with a towel designed for polish removal or at least a high quality microfiber towel.
2) continue until the entire car has been polished. If there is a section that needs a second treatment, do it so the surface appears uniform all over. Don't worry about polishing the clear coat away, or burning the surface. If you use a random orbital, that simply won't happen.
Now, your surface is free, smooth, and ready to absorb a good quality wax. On to the final step.
WAX:
Some important info: NEVER use cheap parts store sealants that promise a year of protection. Thees products will likely seal the surface, prevent the surface from breathing, and can permanently damage the clear coat. Suffice to say that if you buy a $10 wax, you will get a $10 quality and performance.
1) Use a wax that has a significant amount of 'pure carnuba'. Carnuba is like a steel shield that still allows the surface to breath. Apply the wax VERY lightly. The surface will only accept a certain amount of wax - anything over that amount will be a waste and make removal and buffing a very difficult chore.
2) apply and remove/ buff in small sections (one fender, 1/4 of the roof, etc). Use high quality cloth - extra thick microfiber for example and turn the cloth frequently and change towels as you proceed. I use at least 4 cloths - one for the roof and trunk, one for the hood and bumpers, one for left side panels, one for right side panels.
If you spend a day doing this, you will be floored by the results. It should last about 4-6 months and you will be protecting the surface in addition to just shining it.
Products:
I use only Griot's Garage. Anyone as anal as I am about doing this will likely have a favorite company as well.
https://www.griotsgarage.com/ for videos on how to use these products
for washing: Griot's Car Wash
for clay bar: Griot's Clay, Speed Shine for lubricant + PFM detailing towels
for polish: Griot's Boss Correcting Cream + orange foam correcting pad
for wax: Griot's Best Of Show Wax + red foam waxing pad
Tools:
Griot's random orbital 6" model and 3" model (3" model isn't required - i just like it for smaller areas like the bumpers, etc)
microfiber polish removal cloths
dual weave wax removal cloths
cotton buffing cloths
I cannot tell you how many people compliment me on the finish of my car. It out-shines brand new cars at the dealer and they are floored when I tell them the car is 7 years old and has not been garage kept.