how do you determine how many sounds a word has? I know how to tell how many syllables it has, but not the sounds.

The only way to determine number of sounds is to say the word out loud.

For instance "cough" only has 3 sounds.
(k aw f)

"brought" has 4 sounds (b r aw t)

"book" has 3 sounds (b oo k)

You can look into some dictionaries and they will give you the sounds.