for ps3 development you need to buy ps3 dev kit, which is cost around $2000. it includes hardware and software for development. the software includes sdk where you can code in c++ ( or some other languages sony specifies ). and the graphics library to use is PSGL ( PlayStation Graphics Library ). that is a combination of OpenGL-ES and the CG programming of NVIDIA. and later to release the game you need to become sony licensed developer. for that you should contact sony through mail. that license is given only to developers or developer team which is having enough previous understanding in game development.
and now (around the feb '12 ) sony is going to release playstation suite by which developers can able to develop applications and games for playstation certified devices ( ps3, playstation vita, some android mobiles, etc ). there you have to use c# to code. but afaik it will not be a better sdk for full fledged AAA game development for ps3. Because it uses a virtual machine which translates the code dynamically to the underlying hardware platform where it runs, which may affect the performance. and the sdk is now in closed beta test for developers in us, uk, japan. you can get results regarding this from google with query 'playstation suite closed beta'. and its beta is expected to be released in the coming feb with the release of playstation vita.
for microsoft xbox 360 better place to start is xna game development. and after some time getting better knowledge in game development, you can approach microsoft to get the sdk for xbox 360 game development. the games developed with xna will not be much faster as games developed with the sdk given by microsoft. but getting the sdk for xbox is also having lots of procedures as getting sdk for ps3. the xna coding will be in c# with directx and direct3d as graphics library.
and later news tells that microsoft is migrating to metro style apps from xna. metro is going to be released with windows 8. now its beta version is bundled with windows 8 beta release. and microsoft doesn't show any support for xna in future ( it is not clear still ). now xna is only available for dircetx9. but metro is going to be released with directx11. microsoft didn't give any word about xna support in future. in metro apps, you need to be code in C++ with directx and direct3d graphics libraries.