Improve is pronounced /ɪmˈpruːv/, with the stress on the second syllable: im-PROOVE. Dictionaries verify this stress pattern through the closely related word improvement, which keeps the same im-PROOVE stem, so you can rely on the pattern applying to improve itself. This is the usual pronunciation in everyday use.
On variety: Cambridge shows identical UK and US transcriptions for improvement, and no difference is documented for improve itself.
Mouth movements
Start with a short ih, tongue high and forward in your mouth, then close your lips on the m. Keep this first syllable quick and light.
Next comes the r sound: curl the sides of your tongue up without letting your lips touch again. Then push your lips forward into a tight round shape for oo, as in too. The rounding belongs to the vowel, so it happens after the r, not before it.
Finish with a soft v: top teeth rest lightly on the bottom lip and you buzz. Let the second syllable carry the full stress, so it sounds like im-PROOVE, never IM-proove.
Say it in a phrase
Stress pruuv so it sounds longer and slightly louder than im, then say: We want to improve. The sentence leans on -PROOVE.
Try a gentle request: Could I improve this? Keep pruuv long and strong, and let im stay quick and quiet inside the question.
Beside the sound, notice where the strong vowel sits: in improve, the strong vowel lives in the second syllable, im-PROOVE, so im stays quick and light.
One more word to read aloud: improve. Say We want to improve, and feel the strong syllable land on the second part, im-PROOVE, the opposite side from where it falls in impair.