How many phonemes are there in the word "dogs"?
Phonemes are the smallest distinguishable sounds in words, basically. Though case has four letters (or graphemes) , there are only three phonemes, or sounds: c, a, and s. Since the grapheme e is not heard in speech, there is no corresponding phoneme.
In dogs, there are four phonemes: d, o, g, and s. Each phoneme makes a sound distinct from the others.
For better coverage of what counts as an English phoneme, this pdf (not mine-- unearthed with the aid of Google) might be useful.
As the disclaimer says at the bottom, the number of phonemes in English varies depending on who you ask, but it gives you a pretty fair idea.