How to pronounce "linearly"?

Solution 1:

The CMU Pronouncing Dictionary gives an American English pronunciation for linearly: http://www.speech.cs.cmu.edu/cgi-bin/cmudict/?in=linearly&stress=-s

L IH1 N IY0 ER0 L IY0

In International Phonetic Alphabet (IPA) this would be /ˈlɪniːɚliː/

In the American Heritage Dictionary-style pronunciation respelling it would be \lĭnēərlē\

In the Wikipedia pronunciation respelling style it would be _^LIN-ee-er-lee

As has been discussed in other answers, in standard non-rhotic British English, the 'er' of the third syllable is pronounced non-rhotically—that is, indistinguishable from an ordinary schwa. However, there are a number of rhotic British English dialects with a substantial number of speakers which would pronounce the 'er' rhotically.

Solution 2:

Probably /'lɪnɪəlɪ/ (depending on your dialect of English). Four phonemes (sounds), anyway: LI-nee-uh-li.

In fact, there is some pronunciation help online: http://oxforddictionaries.com/definition/english/linear?q=linearly#linear__9 and it looks like ODO agrees with me as far as British English is concerned.

Help on IPA symbols