You're title says "best IDE to swing", and your thread asks for an API.
Are you asking "What is the best IDE to use to create swing applications?".
If so then it is down to personal choice, myself i use Netbeans, as i find it is incredibily easy to use and you can implement features simply without having to write lines and lines of code, for example handling events for certain components.
1) It is Swing, not swing.
2) If you need to ask that question, I would say the best approach is "brain + Swing tutorial". Trying to code Swing GUIs in an IDE before you understand how layouts and Swing works, will get you into a whole heap of trouble that you are unable to resolve, and produce code that others will not be willing to wade through.
3) The 'best' IDE, as already mentioned, is entirely subjective. Netbeans and Eclipse are two IDEs often recommended, with JCreator probably coming in 3rd (a long way behind the other two). Or to be more accurate, those IDEs are the most mentioned in my perception across various public forums. The first two are probably often used simply because they are free. ;)