Q: What are the right steps to move iTunes 11 library from external HD to internal HD?

Drag the entire iTunes folder to the internal drive, launch iTunes with the Option key held down, and choose that library.

(111257)

What exactly do you have on the external drive?  A library is more than just media files.

Quick answer if you use iTunes' default preferences settings:  Copy the entire iTunes folder (and in doing so all its subfolders and files) intact to the other drive.  Open iTunes and immediately hold down the option (alt) key (shift on Windows) so you get a prompt to choose a library, then select the copied iTunes folder.

If this is to a new computer and you put the copied iTunes folder in the default location of Macintosh HD > Users > *User Name* > Music  then you don't even need to start with the option key held down, iTunes will automatically look for it there.  (Make sure there isn't anything already in the iTunes folder there that you want to keep since you will be replacing it with the one you are moving.)

What are the iTunes library files? - http://support.apple.com/kb/HT1660

More on iTunes library files and what they do - http://en.wikipedia.org/wiki/ITunes#Media_management

What are all those iTunes files? - http://www.macworld.com/article/139974/2009/04/itunes_files.html

Where are my iTunes files located? - http://support.apple.com/kb/ht1391

iTunes 9 [and later]: Understanding iTunes Media Organization - http://support.apple.com/kb/ht3847 - plus supplemental information about organizing to new structure https://discussions.apple.com/message/26404702#26404702

Image of folder structure and explanation of different iTunes versions (turingtest2 post) - https://discussions.apple.com/docs/DOC-7392 - and making an iTunes library portable.