As per request, here is a bit more detailed explanation of how I went about polishing the car. Before you begin, make sure you mask off all of the plastics, rubbers and glass to avoid damage.
Step 1 - Dry 1500
Go over the car with 1500 grit dry sandpaper. You need to be very careful with this as it is quite easy to strip the clear coat when approaching edges or difficult to reach places. If you have various size heads then I recommend using them or even rubbing by hand will work (just takes more time). This stages allows you to remove any imperfections such as clear coat runs or any bits that might have stuck onto the clear coat while drying.
Once you have gone over the entire car, give it wipe with a MF cloth to see your result. You should not be able to see any shiny spots, and if you do then run over them again till they are matte.
Step 2 - Wet 3000
Once you are done with the 1500 grit, it is time to move onto Wet 3000 grit sandpaper. This is one of the most important stages of this polishing process as it essentially refines the surface and makes the panels smooth to the touch again. Make sure you use plenty of water to lubricate the pad (it is easy to tell when it's lacking).
Again after you believe you have finished with a panel, give it a wipe down with your cloth and check for imperfections.
Step 3 - Wet 6000
Next us is the Wet 6000 grit sandpaper. You don't have to be very careful with this as it is EXTREMELY hard to mess anything up. Simply go around the panels while keeping it reasonably damp and things should start to gloss over after a wipe down. This is what starts to give a really smooth look and finish.
All of the above is done using an orbital dust-free sander. You can of course do this manually by hand but... It will take you a couple of weeks
Step 4 - Compound
After the entire car has had the 6000 treatment, you can now start to bring back that colour and get it shiny looking again. This stage isn't that difficult but it is quite messy. Make sure you have a clean cloth to go over the panels after you are done with them, and repeat over it if it is still hazy. The panels should be crystal clear after this stage. You can use something like 3M Perfect-it III Fast Cut Plus Compound or the Farecla G3 Premium.
Step 5 - High Gloss Polish
This stage will help remove the swirls or pig-tails as detailers call them, that are left behind after the compound stage. It is not messy and should ideally be done using a softer pad on your DA polisher. It also has UV protection too. You can use 3M Perfect-it III Ultrafina SE or equivalent for this.
Step 6 - Speed Wax
This is pretty self explanatory, essentially it is a faster curing Wax for your car. If you have the time for the conventional method, then do that but I chose to go over it with Scholl Concepts SW20 Premium Speed Wax. This was mainly due to the fact that the car was getting ceramic coated anyway so this didn't really matter that much.
Step 7 - Ceramic Coating (optional)
Normally when you get up to the above step, you can stop there and be fine for a very long time. However since I am probably never going to get another chance to do the above (or have the time for it) I decided to add ceramic coating and hydrophobic protection at the same time.
For this I used Gtechniq Crystal Serum Light and EXO V4. They are applied by hand using the lint free pads provided. Because you can easily mess this up, it is best to read up on the application instructions found here:
https://gtechniq.com/products/auto/protect/exterior/paint/crystal-serum-light
It takes 12 hours to cure between products and you should always wipe off any excess material.
And this is pretty much it. You will feel great after as your car will look like new, if not better than new, until of course you get the inevitable stone chip or car park ding and swear to never go through this process again
Hope this was helpful