The word "poem" is typically pronounced with two syllables, with a slight emphasis on the second syllable (pō-əm). However, the word is sometimes pronounced with just one syllable, as if it were "pum," which is how it is sometimes spelled in some contexts; this would be pronounced with one syllable as well.
Ultimately, it depends on the context in which the word is used and the individual's linguistic preferences, so both one and two syllable pronunciations are possible. In most contexts, however, the two-syllable version is more common.
For more information, you can check out this article on English pronunciation, which explains the two different ways of pronouncing "poem":
https://www.thoughtco.com/poem-pronunciation-1688917