It can be done by hand but trust me your arm is going to want to drop off
i made a right mess of my 06 grande using a car wash brush (well it seemed like a good idea till i parked it under the garage canopy with its Sodium lights)
anyhow first you need the car uber clean
https://www.fiatforum.com/car-care/188996-basic-guide-how-clean-your-car.html
https://www.fiatforum.com/miscellaneous-guides/319391-getting-into-detailing.html?p=3181746
so a chemical / clay session is in order
(chemical clean first then clay idea is to remove as much as you can without contact to minimize further damage)
https://www.fiatforum.com/miscellaneous-guides/319391-getting-into-detailing.html?p=3181746
from claying stage you can go 1 of 2 ways although some products merge this step....
Hiding
and
removing
Hiding the marks by the use of a filler heavy product
such as
Autoglyms Super resin polish (this has a slight cut to it)
Bilt Hamber autobalm
and removal using a mild deminishing abrasive compound (you wont remove everything by hand but you can get a fair bit out if you spend the time,,,,,
such as
Meguires scratch-x
or Mernenza polish
http://www.elitecarcare.co.uk/menzerna-final-finish-polish-p0-85-re-5-250ml.php?manufacturers_id=49
(which is what i tend to use by hand for small area scratch removal)
With the filler heavy products its a case of rub in well and buff off....
with the cutting polishes there is a bit more to it.......
Most are based on a "deminishable abrasive"
think of grinding a lump of chalk into concrete (concrete been your car and the chalk been one grain of abrasive) the more you grind it into the concrete the more it crumbles and breaks up as it breaks up it cuts less and less deep
so it starts by been aggressive and can lightly cloud the finish but keep at it and the polish breaks down and slowly clears the clouding it inflicts revealing a shiny car........
as such its imperative to only work in small areas eg 1x1ft and use a very small quantity of polish..
you need some kind of polishing pad the German applicators are good..
http://www.ukcarcare.co.uk/applicator-pads/234-wolfgang-german-applicator.html
the firm side allows you to "work" the polish
so to prime the pad for work a light mist of water or quick detailer spray
and for a 1ft square area 2 smartie size blobs is more than enough...
and get rubbing with firm pressure in circular motion you will slowly notice the polish starts to clear once you are left with what looks like a oily residue with no colour left (that menz polish is a blueish gray colour )
buff off with a microfibre towel and inspect if needed repeat again...
(your looking to work that area for 3-5 mins)
then use a paint cleaner to remove the polishing oils or super resin polish
this is an american company but gives you an idea
then wax up the area you have done... (i did a panel a night after work through the summer) its no quick fix but it can be done
if you find your getting hazing your not working the polish long enough and or are using too much
It will not fully remove every mark but will make it look a lot better