UK: /ˈsɒl.əm.li/. US: /ˈsɑː.ləm.li/. Three syllables, stress on the first: SOL-um-lee. The spelled 'n' has no sound in either variety.
Say SOL with full stress.
Then a relaxed um, lips loose.
End with a light lee.
SOL-um-lee, with the middle said as a soft um and no n sound at all.
Say it step by step
Say SOL with the stress. Open your mouth wide and drop your tongue low, as in solve without the final v. UK has a short rounded 'o', US an open 'ah'. The vowels differ in shape, not just length, so pick your variety and stay with it.
Let the mouth go soft for um. Lips relaxed, tongue resting low, no closing of the lips and no 'n' sound at the end.
Finish with a quick, light lee. Touch the tongue tip briefly behind the top teeth for the l, then smile slightly for the ee. Keep this last syllable weaker than the first.
In a speakable phrase
The first syllable carries the full weight, then the remaining syllables fall away lightly. On its own, say SOL clearly, let em stay soft, and end with a light lee so no n sound appears in the middle.
Sound contrast: solemnly next to slowly. Both words keep first-syllable stress and end in the same lee sound. They differ in two places. Slowly begins with the sl cluster, so the tongue taps behind the teeth for the l. Solemnly has no l there, and its stressed vowel is made with the tongue starting low and open, which is also where the two words' middle vowels differ.