Inflated speculation about the writer stumped the liveliest (9)

'liveliest' is the definition.
('bubbly' can be similar in meaning to 'lively')

'inflated speculation about the writer stumped' is the wordplay.
'inflated speculation' becomes 'bubble' (I can't explain this - if you can you should believe this answer much more).
'about' is an insertion indicator.
'the writer' becomes 'I' (the person who is writing these clues).
'stumped' becomes 'st' (cricket abbreviation).
'bubble' going around 'i' is 'bubblie'.
'bubblie'+'st'='BUBBLIEST'

'the' acts as a link.
This may not be right. It may be part of another bit of the clue.

Can you help me to learn more?