This can be difficult, time and consuming and painful but luckily help is at hand. What is needed is a polishing machine. Many professionals use large and heavy polishers but these are expensive and can do a lot of damage in the wrong hands.
Perhaps better for the average DIYer are the latest Random Orbital Polishers, lightweight yet surprisingly powerful and effective. They are half the weight and cost of the bigger grinder types. If you only want a polisher for the car or maybe your boat and you're not using it all day everyday then these smaller units are just what you need.
The machine is important but also important is the kind of pad and polish you use. Pads are either available made of foam or wool. The foam pads come in different grades depending on whether you are cutting, polishing or waxing.
If the surface you are trying to polish has no shine at all or lots of scratches, you'll need to 'cut' back the surface using a cutting pad and a suitable polish. More about that later. If the surface is still shiny but looking a bit dull, you only need to polish the surface. Once the surface has been polished a wax is applied to protect it.
The foam pads are good but they don't last long, certainly not as long as a well made woollen pad. But the woollen pads are more expensive and they shed their hairs all the time whereas the foam pads have no hair to shed so are cleaner to use. Either system will work well. Both systems are available with a velco back which makes the whole process much faster.
For almost any painted surface or gelcoat I have found that 3M fast cut works swiftly to bring back a shine. I have even used it on totally neglected 15 year old gelcoat and it came up almost as new. Even if the paint is shiny you can still use the fast cut as a polish although you must understand that it is removing some of the paint each time. It is not something you would want to do too often but every now and then is fine.
The only problem with the fast cut is that it is pricey but like all good products it works well and saves time and effort.
You might think that it is quite an investment for something that you won't use often but you will be surprised how often you use it. The fast cut can even polish polycarbonate window materials. The polisher can also be used as a sanding machine, albeit without the benefit of dust extraction. I'm not sure what the manufacturers of the polishing machine would say to that but used correctly there is no reason to use more force sanding than you might polishing.