One way or another, Radovan Karadžić was provided with this identity document:
Which belongs not to him, but to this person:
Or that is at least one of the versions. In another version he assumed the identity of a much younger person who was killed during the siege of Sarajevo.
What is fairly certain is that he did not get the false identity on his own. The answer to the question of how he got it probably depends on when he got it. If it was early on, it could have been as early as 1993 when the younger Dragan Dabić was killed. Then chances are that the documents were provided by Karadžić's fellow criminals in Bosnia. If it was later, and the most frequent guess now seems to be that was in Belgrade from 2005 onward, it would have to have been done by criminals in Serbia. What kind of criminals in Serbia? Follow the paper trail: who issues the documents?