Depends totally on the game. You usually have pretty good chances if the game has a lively modding scene and/or if they build upon a middleware engine, since then, it's quite likely the data format has already been reverse engineered or is even public, and there might already be tools available to get the data out.
And no, the data isn't buried "inside the programs", but you often have binary data packages that contain the runtime data aligned in a way so that big chunks can be read into memory in one continuous stream and deserialised in the format the engine understands/uses at runtime. And most of the time, the package files don't just contain models, but also textures, sounds, etc, in a format optimised for fast streaming. This is usually vastly different from your usual 3D modeling tool file formats, but can be "retranslated" (in the end, on the engine toolset side, there's a process that exports the editor side data to the engine side format, and those steps can be reversed for the most part). The question is if you find a tool for that or if you have to write one yourself (which, when you have no knowledge about the orginal process, can get pretty complicated). Without a tool to do that, it's just a big blob of binary data that you can't read.
So, like I wrote in the beginning, it totally depends on the game.
Sorry for that above paragraph coming out a little jumbled, it's late here and it was a long day at the office today 