Mostly if a country doesn't offer visa on arrival, I don't bother with it. But with Abkhazia being kind of near where I was going to go anyway, and the procedure relatively easy and free, I actually went to the trouble to get a permission to enter.
First you need to obtain permission, which you do by downloading a government form from their web site, filling it out and emailing to them. In about 10 days I got the permission letter back. One of the questions on the form is the range of dates you wish to stay there, and I made the mistake of only applying for dates covering five days. These were the dates I had permission to enter. That was my first mistake. If you want greater flexibility ask for a much longer period.
The bureaucrats often make mistakes – and they did on my permission letter, which caused me grief. I had checked it – it’s all in Russian, and wasn’t sure of part of it – and that was where the mistake was. So use Google Translate (photo function) to translate the Russian on the forms and also the approval letter you receive to ensure you make no mistakes, and that the bureaucrat hasn’t. If they have, get it corrected before you travel there. Obviously you take this permission letter with you, but I found it useful to also take the forms I filled out and emailed to the MFA as well.
Once you have entered the country you need to go to the Ministry of Foreign Affairs within three working days (if memory serves) to apply for your visa. If not, you won’t be able to leave the country, apparently. The MFA is in the capital, Sukhumi.
In Georgia I had heard that there had been border scuffles and that it had been closed, but was currently open. So off I went, and after a longish bus ride, and a short taxi ride, I was at the border - ready to cross from Georgia to Abkhazia at Enguri Bridge.
First, by the side of the road is the Georgian police checkpoint, where they pointed out the paperwork error on my permission form. But they let me continue. By the way, should you want to use a toilet, ask the police and they’ll let you use theirs.
Then you walk across the bridge, which takes about 10 minutes. You can pay for a horse and cart to take you if you wish. Once across you go to a pillbox. The Russian soldier found the same error in my letter. (They'd got my date of birth wrong by a few days.) I showed the original forms I’d filled out to show I’d done it correctly. Also he had a big book of lists of people, and on my entry the data was also correct. After a few phone calls he let me proceed. Next was an office where they went through the same procedure. I was guarded by soldiers with rifles, who seemed very severe and unfriendly at first, but after a few minutes became friendly and curious. One spoke passable English. The official (soldier) asked me if I could speak German (answer - sort of), and then we could communicate. Finally they said it was ok and I walked out into Abkhazia.
There in the parking area was a bus, only one road ahead, and I had a bottle of water and few rubles in my pocket. A new adventure...