Others have mentioned the regs so I will not rehash them.
I am about halfway through the process now and here is my take on it. I am exempt from the formal ground school requirement. I do not think it is possible to take the exams without some sort of training (with the possible exception of the IFR and VFR communications exams). There are enough differences between the FAA way of doing things and the EASA way of doing things that it is easy to get tripped up even when some things seem familiar. On top of that EASA still examines some stuff from the dark ages that nobody has used in more than half a century, stuff that was long considered obsolete when I started flying 30 years ago (yes I am an old guy...).
With that being said, what I have done was purchased the ATPL Digital program from Bristol Ground School. I have gone through that, plus purchased the question bank from Dauntless for use on my iPad. For quick reference I purchased a set of sort of 'Cliff Notes' from Piloten-Training.com. Between those three sources I have been successful on the 8 exams I have taken thus far.
Also be aware that you must apply for the license through the country which holds your medical records, but you can do the theory exams and skills through a different country. Be aware though that all 14 theory exams must be done in one country, so you cannot do seven of them in Poland and the other seven in the UK. But you can do all 14 exams through the UK, skills test through Germany, and then do your medical and apply for the license in France if you really wished to do it that way. Obviously it is far simpler to do it in one country, but there is some flexibility if it suits you better.
In my opinion the UK has been the best country to do the conversion process through. They seem to have more experience with it and the process is streamlined and well laid out. It is a bit more expensive than other countries but you do get what you pay for. It took the UK only two days to approve my waiver for the formal ground school. It took Poland almost nine months to do the same thing and I did not receive it until after I gave up and started the exams through the UK.
Good luck!