Getting on with author, turning mad in Manchester (9)
I believe the answer is:
embarking
'getting on' is the definition.
(embarking is a kind of getting on)
'with author turning mad in manchester' is the wordplay.
'with' means one lot of letters go next to another.
'author' becomes 'me' (the author of the crossword).
'turning' says the letters should be written backwards.
'mad in manchester' becomes 'barking' (I can't explain this - if you can you should give a lot more credence to this answer).
'me' written backwards gives 'em'.
'em'+'barking' is 'EMBARKING'.
Can you help me to learn more?
(Other definitions for embarking that I've seen before include "Going on board" , "Going aboard" , "Joining ship" , "getting on board" , "Starting journey" .)