This is very complicated and varies from State to State. Incorporation requires meeting some base criteria, such as sufficient population size in the proposed incorporated area (usually a few hundred people), and often requires an official act of an elected body. How responsibilities can get allocated technically (i.e. what is legally possible which includes some unusual arrangements in some States) and how those responsibilities get allocated in practice is equally complicated. Generally though, for Federal land, the State has limited authority. They do have indirect authority by virtue of the resources that they do control, such as water, that gives the States practical leverage. Federal land cannot be taxed by the State, so the Federal government subsidizes State property taxes in those States where most of the land is Federal because it is nearly impossible to build a property tax base when 90+% of land in a county is Federal. Not only is there not much property, the fragmentation of the land prevents it from achieving an economically productive critical mass.
Federal land has one important difference from private land or even State land: the regulations regarding management and use are pretty disconnected from the realities of the lands under management or the population that lives there, aggravated by the fact that these decisions are primarily made by people that have live very far away from where most Federal land is located and have no experience with those regions.