The 'su' in 'sumimasen' sounds like the 'su' in 'sugar'.: The "s" is pronounced with a clear "s" sound, not like the "z" sound in "azure."
The 'mi' in 'sumimasen' sounds like the 'mi' in 'milk'.: The "i" is pronounced with a clear "i" sound, not like the "ee" sound in "feet."
The 'ma' in 'sumimasen' sounds like the 'ma' in 'mama'.: The "a" is pronounced with a clear "a" sound, not like the "ah" sound in "father."
The 'se' in 'sumimasen' sounds like the 'se' in 'sense'.: The "se" is pronounced with a clear "se" sound, not like the "zeh" sound in "azure."
The 'n' in 'sumimasen' is pronounced with a slight nasal sound: It's not quite as nasal as the "n" in "sing", but it's not as clear as the "n" in "ten" either.
Putting it all together: The pronunciation of "sumimasen" is roughly: "soo-mee-mah-sen". Some people may nasalize the 'n' at the end. For a precise demonstration of the pronunciation, it's best to consult audio resources or a native speaker of Japanese.