/kən prəˈnaʊns/ in most standard British and American speech. Primary stress falls on nounce, the second syllable of pronounce.
The weak form /kən/ for can is standard here, since it sits unstressed before a verb. Use the strong form /kæn/ only for emphasis, as in I CAN pronounce it.
Let your mouth stay slack for can: the jaw barely opens, and the vowel shrinks to a quick /ə/.
Close your lips for /p/, then release straight into /r/ with the tongue curled back, so pro flows out in one soft push.
Round your lips as the vowel glides from /a/ to /ʊ/, then touch the tongue tip behind your top teeth for the final /ns/ and let the stress land right there.
Say the whole phrase like this: I can pronounce it. Keep can light as /kən/ and let the stress land on nounce.
A useful contrast: strong-form can is /kæn/ when it stands alone or carries emphasis, as in Yes, I CAN pronounce it. Weak /kən/ is the unstressed choice before a verb.
To feel the contrast, whisper can in the weak version, then punch it in the strong version. The vowel opens up, and can takes its own stress, while nounce keeps the main stress in neutral speech.
End the phrase cleanly: ns finishes with your tongue tip behind your top teeth, so pronounce it does not become pronoun sit.